If 5-3-2-a-3-b-2- then find the values of -a- and -b-

5/√(3) √(2) = a√(3) b√(2) 5/√(3) √(2) = a√(3) b√(2) On rationalizing the denominator, 5(√(3)+√(2))/(√(3))^2 (√(2))^2 = a√(3) b√(2) 5√(3)+5√(2)/3 2=a√(3) b ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Geometric Estimation Value of Square Root

If 5/√3-√2=a√...

Question

If $\frac{5}{\sqrt{3} - \sqrt{2}} = a \sqrt{3} - b \sqrt{2}$ , then find the values of 'a' and 'b'.

Open in App

Solution

$\frac{5}{\sqrt{3} - \sqrt{2}} = a \sqrt{3} - b \sqrt{2}$

$\frac{5}{\sqrt{3} - \sqrt{2}} = a \sqrt{3} - b \sqrt{2}$

On rationalizing the denominator,

$\frac{5 (\sqrt{3} + \sqrt{2})}{(\sqrt{3})^{2} - (\sqrt{2})^{2}} = a \sqrt{3} - b \sqrt{2}$

$\frac{5 \sqrt{3} + 5 \sqrt{2}}{3 - 2} = a \sqrt{3} - b \sqrt{2}$

$5 \sqrt{3} + 5 \sqrt{2} = a \sqrt{3} - b \sqrt{2}$

On comparing, we get $a = 5, b = - 5$ .

Suggest Corrections

Similar questions

If $\frac{5}{\sqrt{3} - \sqrt{2}} = a \sqrt{3} - b \sqrt{2}$ , then the values of 'a' and 'b' are _________.

Q. If

\frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} =

a + b \sqrt{3}

, then find the value of a and b

Q. If

\frac{3}{4 \sqrt{5} - \sqrt{3}} + \frac{2}{4 \sqrt{5} + \sqrt{3}} = a \sqrt{5} + b \sqrt{3}

, then find the values of

a

and

b

Q. If

\frac{3 + \sqrt{5}}{2 \sqrt{5} + 3} = a + b \sqrt{5}

, then find the values of irrational numbers a and b.

Q. If

2^{a} + 3^{b} = 17

and

2^{a + 2} - 3^{b + 1} = 5,

then find the value of a and b.

Join BYJU'S Learning Program

If 5√3−√2=a√3−b√2, then find the values of 'a' and 'b'.

5√3−√2=a√3−b√2 5√3−√2=a√3−b√2 On rationalizing the denominator, 5(√3+√2)(√3)2−(√2)2=a√3−b√2 5√3+5√23−2=a√3−b√2 5√3+5√2=a√3−b√2 On comparing, we get a=5,b=−5.

If $\frac{5}{\sqrt{3} - \sqrt{2}} = a \sqrt{3} - b \sqrt{2}$ , then find the values of 'a' and 'b'.