Simplify. Remove all perfect squares from inside the square roots. Assume a and b are positive. sqrt(42a^(4)b^(6))=

Identify Perfect Squares: To simplify sqrt(42a^(4)b^(6)), we need to identify and take out the perfect squares from under the square root. sqrt(42a^(4)b^(6)) = sqrt(2 * 3 * 7 * a^(4) * b^(6)) We can see that a^(4) and b^(6) are perfect squares because a^(4) = (a^2)^2 and b^(6) = (b^3)^2.Take Square Roots: Now we take the square root of the perfect squares a^(4) and b^(6). sqrt(a^(4)) = a^2 and sqrt(b^(6)) = b^3. So, we can rewrite the expression as: sqrt(42a^(4)b^(6)) = sqrt(2 * 3 * 7) * sqrt(a^(4)) * sqrt(b^(6)) = sqrt(42) * a^2 * b^3.Final Simplification: Since 42 does not have any perfect square factors other than 1, we cannot simplify sqrt(42) any further. Therefore, the simplified form of the original expression is: sqrt(42a^(4)b^(6)) = sqrt(42) * a^2 * b^3.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify.
Remove all perfect squares from inside the square roots. Assume
a and
b are positive.

sqrt(42a^(4)b^(6))=

Simplify. $\newline$ Remove all perfect squares from inside the square roots. Assume $\newline$ $a$ and $\newline$ $b$ are positive. $\newline$ $\sqrt{42a^{4}b^{6}}$ =

View step-by-step help

Home

Math Problems

Algebra 1

Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square roots. Assume

\newline

a

and

\newline

b

are positive.

\newline

\sqrt{42a^{4}b^{6}}

Identify Perfect Squares: To simplify $\sqrt{42a^{4}b^{6}}$ , we need to identify and take out the perfect squares from under the square root. $\sqrt{42a^{4}b^{6}} = \sqrt{2 \times 3 \times 7 \times a^{4} \times b^{6}}$ We can see that $a^{4}$ and $b^{6}$ are perfect squares because $a^{4} = (a^{2})^{2}$ and $b^{6} = (b^{3})^{2}$ .
Take Square Roots: Now we take the square root of the perfect squares $a^{4}$ and $b^{6}$ . $\newline$ $\sqrt{a^{4}} = a^2$ and $\sqrt{b^{6}} = b^3$ . $\newline$ So, we can rewrite the expression as: $\newline$ $\sqrt{42a^{4}b^{6}} = \sqrt{2 \times 3 \times 7} \times \sqrt{a^{4}} \times \sqrt{b^{6}} = \sqrt{42} \times a^2 \times b^3.$
Final Simplification: Since $42$ does not have any perfect square factors other than $1$ , we cannot simplify $\sqrt{42}$ any further. $\newline$ Therefore, the simplified form of the original expression is: $\newline$ $\sqrt{42a^{4}b^{6}} = \sqrt{42} \times a^{2} \times b^{3}.$