Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Assume $n$ is greater than or equal to zero. $\newline$ $\sqrt{75n^7}$

View step-by-step help

View step-by-step help

Simplify radical expressions with variables

Full solution

Q. Simplify. Assume

n

is greater than or equal to zero.

\newline

\sqrt{75n^7}

Factorization and Pairing: Factor $75n^7$ into its prime factors and pair the factors to form perfect squares where possible. $\newline$ $75$ can be factored into $3 \times 5 \times 5$ , and $n^7$ can be written as $n^6 \times n$ , where $n^6$ is a perfect square since it has an even exponent. $\newline$ So, we have $\sqrt{75n^7} = \sqrt{3 \times 5^2 \times n^6 \times n}$ .
Separation of Squares: Separate the perfect squares from the non-perfect squares inside the square root. We can rewrite the expression as $\sqrt{5^2 \times n^6} \times \sqrt{3n}$ .
Simplification: Simplify the square root of the perfect squares. $\newline$ Since $\sqrt{5^2}$ is $5$ and $\sqrt{n^6}$ is $n^3$ (because the square root of $n^6$ is the number $n$ raised to the power of $\frac{6}{2}$ , which is $3$ ), we get: $\newline$ $5 \times n^3 \times \sqrt{3n}$ .
Final Expression: Write the final simplified expression. $\newline$ The final simplified expression is $5n^3 \cdot \sqrt{3n}$ .

More problems from Simplify radical expressions with variables

Question

\newline

\sqrt{\frac{9}{25}}

\newline

Posted 2 months ago

Question

\newline

1,000

\text{ milligrams}

\_\_\_\_

\text{ grams}

Posted 2 months ago

Question

3

-gallon bottle of bleach costs

\$11.52

. What is the price per quart?

\newline

Posted 2 months ago

Question

Maureen can't wait to make chocolate chip zucchini bread with zucchini from her garden. Her recipe calls for

8

ounces of chocolate chips per loaf. If she has enough zucchini to make

4

loaves of zucchini bread, how many pounds of chocolate chips does she need?

\newline

Hint: There are

16

1

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

Posted 2 months ago

Question

A whale is swimming due north at a speed of

30

miles per hour. Just

5

miles away, a whale-watching tour boat is traveling south, directly toward the whale, at a speed of

46

miles per hour. How long will it be before they meet? If necessary, round your answer to the nearest minute.

\_\_\_\_

\_\_\_\_

Posted 2 months ago

Question

\newline

500

=

Posted 3 months ago

Question

\newline

2,000

=

Posted 3 months ago

Question

\newline

750

=

Posted 3 months ago

Question

\newline

1,500

=

Posted 3 months ago

Question

\newline

1,500

=

Posted 3 months ago