Question

answer fast and help me​

Answer 1

Step-by-step explanation:

here in numerator( a-b) ² identity is used

hope this helps

Answer 2

Operations on Real Numbers

We are asked to evaluate the value of √(√3 – 1/√3 + 1) when the value of √3 is 1.732.

Concerning the answer, we need to rationalize the fractions been operated on and then substituting the value of √3 in their places. Let's start solving!

In order to rationalize the denominator, multiply the rationalising factor with both the numerator and the denominator of the fraction so that you get a rational number in the denominator.

The rationalising factor of the given expression is (√3 – 1). Multiply this with both the numerator and the denominator.

$\sf \sqrt{ \dfrac{ \sqrt{3} - 1 }{ \sqrt{3} + 1 } \times \dfrac{ \sqrt{3} - 1 }{ \sqrt{3} - 1 } }$

Note: Do not exclude the root above √3 – 1/√3 + 1 while rationalising.

Now rearrange the terms to multiply them.

$\sf{ \sqrt{ \dfrac{ { (\sqrt{3} - 1 )}^{2} }{( \sqrt{3} + 1 )( \sqrt{3} - 1)} } }$

To further simplify the numerator and the denominator, use the identity (a + b)² = a² – 2ab + b² for the numerator and (a + b)(a – b) = a² – b² for the denominator, where 'a' and 'b' will be √3 and 1, respectively.

$\sf{ \sqrt{ \dfrac{ { (\sqrt{3})^{2} - 2( \sqrt{3})(1) + (1)}^{2}}{ {( \sqrt{3} )}^{2} - {(1)}^{2} }}}$

Perform the operations so that you will be resulted with the expression given below.

$\sf{ \sqrt{ \dfrac{ { 3 - 2\sqrt{3} + 1}}{ 3 - 1 }}}$

Now, rearrange the terms as it helps you to simply them without confusing.

$\sf{ \sqrt{ \dfrac{ { 3 + 1 - 2\sqrt{3}}}{ 3 - 1 }}}$

Perform addition and subtraction wherever required in both the numerator and the denominator.

$\sf{ \sqrt{ \dfrac{ { 4 - 2\sqrt{3}}}{2 }}}$

You need to expand the numerator by writing it's common factor.

$\sf{ \sqrt{ \dfrac{ { 2(2 -\sqrt{3})}}{2 }}}$

Finally, cancel 2 from both the numerator and the denominator and substitute the value of √3 in its place.

$\sf{ \sqrt{2 - 1.732 } = \underline{\boxed {\bf\red{ 0.517}}}}$

Therefore, the required answer will be 0.517.