Question

root 125 x 5 x 45 x 75 = 375 root 15
how did we get that answer .......

Answer 1

SOLUTION

TO PROVE

$\sf{ \sqrt{(125 \times 5 \times 45 \times 75)} = 375 \sqrt{15} }$

PROOF

$\sf{ \sqrt{(125 \times 5 \times 45 \times 75)} }$

$\sf{ = \sqrt{5 \times 5 \times 5\times 5 \times 5 \times 3 \times 3 \times 5 \times 5 \times 3} }$

$\sf{ = \sqrt{ {5}^{2} \times {5}^{2} \times 5 \times {3}^{2} \times {5}^{2} \times 3} }$

$\sf{ = \sqrt{ {5}^{2} \times {5}^{2} \times {3}^{2} \times {5}^{2} \times 5 \times 3} }$

$\sf{ =( 5 \times 5 \times 5 \times 3)\sqrt{(5 \times 3)} }$

$\sf{ =375 \sqrt{15} }$

Hence proved

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