Question

find the square root of 12+2 under root 35

​

Answer 1

Step-by-step explanation:

=(12+2√35)^2

=(14)^2+35

=196+35

=231

is this helpful to you

for more answers

follow me ❤️

Answer 2

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.