Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Assuming
x and
y are both positive, write the following expression in simplest radical form.

x^(2)y^(2)sqrt(24x^(4)y^(2))
Answer:

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $x^{2} y^{2} \sqrt{24 x^{4} y^{2}}$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Simplify radical expressions with root inside the root

Full solution

Q. Assuming

x

and

y

are both positive, write the following expression in simplest radical form.

\newline

x^{2} y^{2} \sqrt{24 x^{4} y^{2}}

\newline

Answer:

Express in Exponential Form: First, let's express the square root in exponential form and then combine the exponents with the same base. $\newline$ $x^{2}y^{2}\sqrt{24x^{4}y^{2}}$ $\newline$ = $x^{2}y^{2}(24x^{4}y^{2})^{\frac{1}{2}}$
Apply Power Rules: Now, apply the power to a product rule and the power to a power rule to the expression inside the square root. $\newline$ $(24x^{4}y^{2})^{\frac{1}{2}}$ $\newline$ = $24^{\frac{1}{2}}$ * $(x^{4})^{\frac{1}{2}}$ * $(y^{2})^{\frac{1}{2}}$ $\newline$ = $2$ * $\sqrt{6}$ * $x^{2}$ * $y$
Multiply Inside and Outside: Next, multiply the expression obtained from the square root with the terms outside the square root. $\newline$ $x^{2}y^{2} \times (2 \times \sqrt{6} \times x^{2} \times y)$ $\newline$ = $2 \times x^{2} \times x^{2} \times y^{2} \times y \times \sqrt{6}$
Combine Like Terms: Combine the like terms by adding the exponents for the bases $x$ and $y$ . $\newline$ = $2 \times x^{(2+2)} \times y^{(2+1)} \times \sqrt{6}$ $\newline$ = $2 \times x^{4} \times y^{3} \times \sqrt{6}$
Simplify Radical Form: The expression is now simplified to its simplest radical form.

More problems from Simplify radical expressions with root inside the root

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

Multiply. Write your answer in simplest form.

\newline

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

\newline

Posted 1 month 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