Question

root 10 into root 15 ​

Answer 1

Answer:

$\sqrt{10} \times \sqrt{15 } = \sqrt{150}$

Answer 2

Answer:

$\blue{\sqrt{10}\sqrt{15}=5\sqrt{6}\quad \left(\mathrm{Decimal:\quad }\:12.24745\dots \right)}$

Step-by-step explanation:

$\sqrt{10}\sqrt{15}$

$\gray{\mathrm{Factor\:integer\:}10=5\cdot \:2}$

$=\sqrt{5\cdot \:2}\sqrt{15}$

$\gray{\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}}$

$\gray{\sqrt{5\cdot \:2}=\sqrt{5}\sqrt{2}}$

$=\sqrt{5}\sqrt{2}\sqrt{15}$

$\gray{\mathrm{Factor\:integer\:}15=5\cdot \:3}$

$=\sqrt{5}\sqrt{2}\sqrt{5\cdot \:3}$

$\gray{\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}}$

$\gray{\sqrt{5\cdot \:3}=\sqrt{5}\sqrt{3}}$

$=\sqrt{5}\sqrt{2}\sqrt{5}\sqrt{3}$

$\gray{\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{a}=a}$

$\gray{\sqrt{5}\sqrt{5}=5}$

$=5\sqrt{2}\sqrt{3}$

$\gray{\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{b}=\sqrt{ab}}$

$\gray{\sqrt{2}\sqrt{3}=\sqrt{2\cdot \:3}}$

$=5\sqrt{2\cdot \:3}$

$\gray{\mathrm{Multiply\:the\:numbers:}\:2\cdot \:3=6}$

$=5\sqrt{6}$