Question

find the sq root of 28+10√3​

Answer 1

Answer:

5+3^(1/2)

Step-by-step explanation:

To find the square root of the term 28+10*3^(1/2)          (1)

Let's try to break the equation in the form of

(a+b)^2=a^2+b^2+2ab              (2)

Let's Compare the equations (1) and (2)

we get

a^2+b^2=28              (3)

2ab=10*3^(1/2)           (4)  

Solving this equation further we get

ab=5*3^(1/2)

If we consider

a= 5 and b=3^(1/2)

putting the values in equation(3) the values are verified as we get

a^2+b^2=28  

5^2+$\sqrt{3}$^(2)=28

writing the equation in equation (2) format we get

5^2+($\sqrt{3}$)^2+2*5*$\sqrt{3}$= (5+$\sqrt{3}$)^2

Hence taking the square root of RHS we get

square root of(28+10$\sqrt{3}$)= 5+$\sqrt{3}$

Hence the answer is 5+$\sqrt{3}$