Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Multiply. Write your answer in simplest form. $\newline$ $\sqrt{273} \times \sqrt{42}$ $\newline$ ______

View step-by-step help

View step-by-step help

Multiply radical expressions

Full solution

Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{273} \times \sqrt{42}

\newline

______

Find prime factorization: Find the prime factorization of the numbers under the square roots to simplify the expression. The prime factorization of $273$ is $3 \times 7 \times 13$ , and the prime factorization of $42$ is $2 \times 3 \times 7$ . So, $\sqrt{273} \times \sqrt{42}$ can be expressed as $\sqrt{3 \times 7 \times 13} \times \sqrt{2 \times 3 \times 7}$ .
Combine square roots: Apply the multiplication property of square roots to combine the two square roots into one. This gives us $\sqrt{3 \times 7 \times 13} \times \sqrt{2 \times 3 \times 7} = \sqrt{3 \times 7 \times 13 \times 2 \times 3 \times 7}$ .
Group perfect square factors: Group the perfect square factors together within the square root. We have $\sqrt{3 \times 7 \times 13 \times 2 \times 3 \times 7} = \sqrt{2 \times 13 \times 3^2 \times 7^2}$ .
Extract perfect square factors: Extract the perfect square factors from the square root. The square root of a perfect square is the base of that square. So, $\sqrt{2 \times 13 \times 3^2 \times 7^2} = 3 \times 7 \times \sqrt{13 \times 2}$ because $3^2$ and $7^2$ are perfect squares.
Simplify the expression: Simplify the expression by multiplying the numbers outside the square root and keeping the square root as is. So, $3 \times 7 \times \sqrt{13 \times 2}$ simplifies to $21 \times \sqrt{26}$ .

More problems from Multiply radical expressions

Question

Find the real-number root.

\newline

\sqrt{16}

\newline

\newline

Write your answer in simplified form.

\newline

\_\_\_\_

Posted 2 months ago

Question

Find the real-number root.

\newline

\sqrt{\frac{9}{16}}

\newline

Simplify your answer and write it as a decimal or as a proper or improper fraction.

\newline

\_\_\_\_\_

Posted 2 months ago

Question

Find the real-number root using a calculator. Round your answer to the nearest thousandth.

\newline

\newline

Posted 2 months ago

Question

\newline

\sqrt{\frac{63}{4}}

\newline

Posted 2 months ago

Question

Simplify. Rationalize the denominator.

\newline

\frac{-4}{9 - \sqrt{2}}

\newline

Posted 2 months ago

Question

z

\newline

16 = \sqrt{z}

\newline

z =

Posted 2 months ago

Question

Simplify the radical expression.

\sqrt{14x^{14}}

Write your answer in the form

A

\sqrt{B}

A\sqrt{B}

A

B

are constants or expressions in

x

. Use at most one radical in your answer, and at most one absolute value symbol in your expression for

A

Posted 2 months ago

Question

Simplify the radical expression.

\newline

\sqrt{12x^{12}}

\newline

Write your answer in the form

A

\sqrt{B}

A\sqrt{B}

A

B

are constants or expressions in

x

. Use at most one radical in your answer, and at most one absolute value symbol in your expression for

A

\newline

\underline{\hspace{3cm}}

Posted 2 months ago

Question

What is the value of

\sin \left(\frac{5 \pi}{6}\right) ?

\newline

1

\newline

-\frac{\sqrt{3}}{2}

\newline

-\frac{\sqrt{2}}{2}

\newline

\frac{1}{2}

\newline

150

Posted 4 months ago

Question

56x8

Posted 8 hours ago