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$root is the product of n quad1 fractions.) The value of n is (A) 81 (B) 64 (C) 16 (D) 256 (E) 100$

root is the product of $n \quad 1$ fractions.) The value of $n$ is $\newline$ (A) $81$ $\newline$ (B) $64$ $\newline$ (C) $16$ $\newline$ (D) $256$ $\newline$ (E) $100$

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Math Problems

Algebra 2

Roots of rational numbers

Full solution

Q. root is the product of

n \quad 1

fractions.) The value of

n

\newline

(A)

81

\newline

(B)

64

\newline

(C)

16

\newline

(D)

256

\newline

(E)

100

Calculate product: Calculate the product of one quad $1$ fraction. $\newline$ $1 \times 1 = 1$
Identify perfect square: Since we need the product of $n$ $\text{quad}_1$ fractions to be a root, $n$ must be a perfect square. $\newline$ Look for the perfect square among the options.
Check options: Option (A) $81$ is a perfect square because $9 \times 9 = 81$ .
Find quad $1$ product: Option (B) $64$ is also a perfect square because $8 \times 8 = 64$ .
Evaluate square roots: Option (C) $16$ is a perfect square because $4 \times 4 = 16$ .
Evaluate square roots: Option (C) $16$ is a perfect square because $4 \times 4 = 16$ . Option (D) $256$ is a perfect square because $16 \times 16 = 256$ .
Evaluate square roots: Option (C) $16$ is a perfect square because $4 \times 4 = 16$ . Option (D) $256$ is a perfect square because $16 \times 16 = 256$ . Option (E) $100$ is a perfect square because $10 \times 10 = 100$ .
Evaluate square roots: Option (C) $16$ is a perfect square because $4 \times 4 = 16$ . Option (D) $256$ is a perfect square because $16 \times 16 = 256$ . Option (E) $100$ is a perfect square because $10 \times 10 = 100$ . Since all options are perfect squares, we need to find which one is the product of quad $1$ fractions. $\newline$ A quad $1$ fraction is a fraction where both the numerator and denominator are $1$ .
Evaluate square roots: Option (C) $16$ is a perfect square because $4 \times 4 = 16$ . Option (D) $256$ is a perfect square because $16 \times 16 = 256$ . Option (E) $100$ is a perfect square because $10 \times 10 = 100$ . Since all options are perfect squares, we need to find which one is the product of quad $1$ fractions. $\newline$ A quad $1$ fraction is a fraction where both the numerator and denominator are $1$ . The product of $n$ quad $1$ fractions would be $1^n$ , which is always $1$ . $\newline$ So we need to find which option equals $1$ when taking the square root.
Evaluate square roots: Option (C) $16$ is a perfect square because $4 \times 4 = 16$ . Option (D) $256$ is a perfect square because $16 \times 16 = 256$ . Option (E) $100$ is a perfect square because $10 \times 10 = 100$ . Since all options are perfect squares, we need to find which one is the product of quad $1$ fractions. $\newline$ A quad $1$ fraction is a fraction where both the numerator and denominator are $1$ . The product of $n$ quad $1$ fractions would be $1^n$ , which is always $1$ . $\newline$ So we need to find which option equals $1$ when taking the square root. The square root of $4 \times 4 = 16$ $1$ is $4 \times 4 = 16$ $2$ , not $1$ .
Evaluate square roots: Option (C) $16$ is a perfect square because $4 \times 4 = 16$ . Option (D) $256$ is a perfect square because $16 \times 16 = 256$ . Option (E) $100$ is a perfect square because $10 \times 10 = 100$ . Since all options are perfect squares, we need to find which one is the product of quad $1$ fractions. $\newline$ A quad $1$ fraction is a fraction where both the numerator and denominator are $1$ . The product of $n$ quad $1$ fractions would be $1^n$ , which is always $1$ . $\newline$ So we need to find which option equals $1$ when taking the square root. The square root of $4 \times 4 = 16$ $1$ is $4 \times 4 = 16$ $2$ , not $1$ . The square root of $4 \times 4 = 16$ $4$ is $4 \times 4 = 16$ $5$ , not $1$ .
Evaluate square roots: Option (C) $16$ is a perfect square because $4 \times 4 = 16$ . Option (D) $256$ is a perfect square because $16 \times 16 = 256$ . Option (E) $100$ is a perfect square because $10 \times 10 = 100$ . Since all options are perfect squares, we need to find which one is the product of quad $1$ fractions. $\newline$ A quad $1$ fraction is a fraction where both the numerator and denominator are $1$ . The product of $n$ quad $1$ fractions would be $1^n$ , which is always $1$ . $\newline$ So we need to find which option equals $1$ when taking the square root. The square root of $4 \times 4 = 16$ $1$ is $4 \times 4 = 16$ $2$ , not $1$ . The square root of $4 \times 4 = 16$ $4$ is $4 \times 4 = 16$ $5$ , not $1$ . The square root of $16$ is $4 \times 4 = 16$ $8$ , not $1$ .
Evaluate square roots: Option (C) $16$ is a perfect square because $4 \times 4 = 16$ . Option (D) $256$ is a perfect square because $16 \times 16 = 256$ . Option (E) $100$ is a perfect square because $10 \times 10 = 100$ . Since all options are perfect squares, we need to find which one is the product of quad $1$ fractions. $\newline$ A quad $1$ fraction is a fraction where both the numerator and denominator are $1$ . The product of $n$ quad $1$ fractions would be $1^n$ , which is always $1$ . $\newline$ So we need to find which option equals $1$ when taking the square root. The square root of $4 \times 4 = 16$ $1$ is $4 \times 4 = 16$ $2$ , not $1$ . The square root of $4 \times 4 = 16$ $4$ is $4 \times 4 = 16$ $5$ , not $1$ . The square root of $16$ is $4 \times 4 = 16$ $8$ , not $1$ . The square root of $256$ is $16$ , not $1$ .
Evaluate square roots: Option (C) $16$ is a perfect square because $4 \times 4 = 16$ . Option (D) $256$ is a perfect square because $16 \times 16 = 256$ . Option (E) $100$ is a perfect square because $10 \times 10 = 100$ . Since all options are perfect squares, we need to find which one is the product of quad $1$ fractions. $\newline$ A quad $1$ fraction is a fraction where both the numerator and denominator are $1$ . The product of $n$ quad $1$ fractions would be $1^n$ , which is always $1$ . $\newline$ So we need to find which option equals $1$ when taking the square root. The square root of $4 \times 4 = 16$ $1$ is $4 \times 4 = 16$ $2$ , not $1$ . The square root of $4 \times 4 = 16$ $4$ is $4 \times 4 = 16$ $5$ , not $1$ . The square root of $16$ is $4 \times 4 = 16$ $8$ , not $1$ . The square root of $256$ is $16$ , not $1$ . The square root of $100$ is $256$ $4$ , not $1$ .
Evaluate square roots: Option (C) $16$ is a perfect square because $4 \times 4 = 16$ . Option (D) $256$ is a perfect square because $16 \times 16 = 256$ . Option (E) $100$ is a perfect square because $10 \times 10 = 100$ . Since all options are perfect squares, we need to find which one is the product of quad $1$ fractions. $\newline$ A quad $1$ fraction is a fraction where both the numerator and denominator are $1$ . The product of $n$ quad $1$ fractions would be $1^n$ , which is always $1$ . $\newline$ So we need to find which option equals $1$ when taking the square root. The square root of $4 \times 4 = 16$ $1$ is $4 \times 4 = 16$ $2$ , not $1$ . The square root of $4 \times 4 = 16$ $4$ is $4 \times 4 = 16$ $5$ , not $1$ . The square root of $16$ is $4 \times 4 = 16$ $8$ , not $1$ . The square root of $256$ is $16$ , not $1$ . The square root of $100$ is $256$ $4$ , not $1$ . None of the options give a square root of $1$ , so there seems to be a mistake in the reasoning. $\newline$ Re-evaluate the understanding of the problem.

root is the product of n1 n \quad 1 n1 fractions.) The value of n n n is\newline(A) 818181\newline(B) 646464\newline(C) 161616\newline(D) 256256256\newline(E) 100100100

root is the product of $n \quad 1$ fractions.) The value of $n$ is $\newline$ (A) $81$ $\newline$ (B) $64$ $\newline$ (C) $16$ $\newline$ (D) $256$ $\newline$ (E) $100$