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

8x^(2)sqrt(252x^(2)y^(4))
Answer:

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $8 x^{2} \sqrt{252 x^{2} y^{4}}$ $\newline$ Answer:

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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

8 x^{2} \sqrt{252 x^{2} y^{4}}

\newline

Answer:

Factorize Number: Factor the number inside the square root to prime factors. $\newline$ We need to factor $252$ to simplify the square root. $\newline$ $252 = 2 \times 126$ $\newline$ $= 2 \times 2 \times 63$ $\newline$ $= 2 \times 2 \times 7 \times 9$ $\newline$ $= 2 \times 2 \times 7 \times 3 \times 3$ $\newline$ $= 2^2 \times 3^2 \times 7$
Simplify Square Root: Simplify the square root by taking out factors that are perfect squares. $\sqrt{252x^{2}y^{4}}$ can be simplified by taking out the square factors. $\sqrt{2^{2} \times 3^{2} \times 7 \times x^{2} \times y^{4}}$ = $2 \times 3 \times x \times y^{2} \times \sqrt{7}$ = $6xy^{2} \times \sqrt{7}$
Multiply Simplified Root: Multiply the simplified square root by the term outside the square root. $\newline$ Now we multiply $8x^{2}$ by the simplified square root from Step $2$ . $\newline$ $8x^{2} \times 6xy^2 \times \sqrt{7}$ $\newline$ $= 48x^{3}y^2 \times \sqrt{7}$

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