Find the square root of 12+2 under root 35

1.	Find the square root of 12+2 under root 35
Answer» Step-by-step: Since $\sf{\sqrt{35} =\sqrt{5} \times\sqrt{7} }$ , there must be two square roots. Let the value $\sf{12+2\sqrt{35} }$ be a square of some number $\sf{\sqrt{a} +\sqrt{b} }$ . $\sf{\implies (\sqrt{a} +\sqrt{b} )^2=12+2\sqrt{35} }$ $\sf{\implies a+2\sqrt{ab} +b=12+2\sqrt{35} }$ $\sf{\implies a+b=12\;and\;ab=35}$ $\sf{\therefore Two\;numbers\;are\;5\;and\;7.}$ So the value was a square of $\sf{\sqrt{7} +\sqrt{5} }$ . Hence the square ROOT of the GIVEN value is $\sf{\sqrt{7} +\sqrt{5} }$ . Learn more: We approach with the ALGEBRAIC identity $\sf{(x+y)^2=x^2+2xy+y^2}$ . And when a number is SQUARED, its square root should be the original number. Extra question: Find the square root of $\sf{12+4\sqrt{3} +4\sqrt{5} +2\sqrt{15} }$ . You could solve this with $\sf{(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx}$ . Hope this helps.

Answer»

Step-by-step:

Since $\sf{\sqrt{35} =\sqrt{5} \times\sqrt{7} }$ , there must be two square roots.