What is sqrt(4p^7q^2+p^4q^2) ?

The solution to sqrt(4p^7q^2+p^4q^2) is p^2qsqrt(4p^3+1)

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simplify sqrt(4p^7q^2+p^4q^2)

simplify

4 p^{7} q^{2} + p^{4} q^{2}

p^{2} q 4 p^{3} + 1

Solution steps

4 p^{7} q^{2} + p^{4} q^{2}

Factor out common term

p^{4} q^{2} : p^{4} q^{2} (4 p^{3} + 1)

= p^{4} q^{2} (4 p^{3} + 1)

p^{4} q^{2} (4 p^{3} + 1) = p^{4} q^{2} 4 p^{3} + 1

= p^{4} q^{2} 4 p^{3} + 1

Simplify

p^{4} : p^{2}

= p^{2} q^{2} 4 p^{3} + 1

Apply radical rule:

a^{2} = a,

assuming

a \geq 0

q^{2} = q

= p^{2} q 4 p^{3} + 1

(b^{- 2})^{- 8}

\frac{8}{8} \div \frac{6}{9}

1.0 6^{2}

8 + (- 15)

1.0 6^{6}

What is sqrt(4p^7q^2+p^4q^2) ?
The solution to sqrt(4p^7q^2+p^4q^2) is p^2qsqrt(4p^3+1)