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How do you simplify $7 \sqrt{63 m^{3} p}$ $7sqrt(63m^3p)$ ?

1 Answer

Mar 9, 2018

$7 \sqrt{63 m^{3} p} = 21 m \sqrt{7 m p}$ $7sqrt(63m^3p)=color(blue)(21msqrt(7mp))$

Explanation:

$63 = 7 \times 9 = 7 \times 3^{2}$ $63=7xx9=7xx3^2$

$m^{3} = m \times m^{2}$ $m^3=mxxm^2$

Therefore $7 \sqrt{63 m^{3} p}$ $7sqrt(63m^3p)$

$XXX = 7 \sqrt{7 \times 3^{2} \times m \times m^{2} \times p}$ $color(white)("XXX")=7sqrt(7xx3^2xxmxxm^2xxp)$

$XXX = 7 \cdot \sqrt{{(3 m)}^{2}} \cdot \sqrt{7 m p}$ $color(white)("XXX")=7 * sqrt((3m)^2) * sqrt(7mp)$

$XXX = 7 \cdot (3 m) \cdot \sqrt{7 m p}$ $color(white)("XXX")=7 * (3m) * sqrt(7mp)$

$XXX = 21 m \sqrt{7 m p}$ $color(white)("XXX")=21msqrt(7mp)$

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