Question

what is the square root of what is the square of root of 126 ​

Answer 1

Answer:

$\sqrt{126}=3\sqrt{14}\quad \left(\mathrm{Decimal:\quad }\:11.22497\dots \right)$

Step-by-step explanation:

$\sqrt{126}$

$\gray{\mathrm{Prime\:factorization\:of\:}126:\quad 2\cdot \:3^2\cdot \:7}$

$=\sqrt{2\cdot \:3^2\cdot \:7}$

$=\sqrt{3^2\cdot \:2\cdot \:7}$

$\gray{\mathrm{Apply\:radical\:rule}:\quad \sqrt{ab}=\sqrt{a}\sqrt{b},\:\quad \:a\ge 0,\:b\ge 0}$

$\gray{\sqrt{3^2\cdot \:2\cdot \:7}=\sqrt{3^2}\sqrt{2\cdot \:7}}$

$=\sqrt{3^2}\sqrt{2\cdot \:7}$

$\gray{\mathrm{Apply\:radical\:rule}:\quad \sqrt{a^2}=a,\:\quad \:a\ge 0}$

$\gray{\sqrt{3^2}=3}$

$=3\sqrt{2\cdot \:7}$

$\gray{\mathrm{Multiply\:the\:numbers:}\:2\cdot \:7=14}$

$=3\sqrt{14}$

Answer 2

Answer:

Step By Step Explanation:

Firstly, Find Prime factorisation of 126

===> Prime factorisation of 126 = 2×3²×7

Then, After resolving 126 into prime factors

√126 = √2×3²×7

√126 = √3²×√2×7 [By applying radical's rule]

√126 = 3×√14

√126 = 3×3.742 [Using table for √14]

√126 = 11.226.

The square root of 126 is 11.226 or 3√14.