If \(x = 11 + 2\sqrt{30}\), then what is the value of \(x^{1/2} + x^{-1/2}\)?
\(2\sqrt{6}\)
\(11 + 2\sqrt{30} = 6 + 5 + 2\sqrt{6}\sqrt{5} = (\sqrt{6}+\sqrt{5})^2\), so \(x^{1/2} = \sqrt{6}+\sqrt{5}\). Then \(x^{-1/2} = \dfrac{1}{\sqrt{6}+\sqrt{5}} = \sqrt{6}-\sqrt{5}\) (rationalising). Therefore \(x^{1/2}+x^{-1/2} = (\sqrt{6}+\sqrt{5}) + (\sqrt{6}-\sqrt{5}) = 2\sqrt{6}\).
Similar Questions
If \(\mathbf{x}^{\mathbf{m}}=\sqrt[14]{\mathbf{x} \sqrt{\mathbf{x} \sqrt{\mathbf{x}}}}\) , then what is the value of m?
If x varies as y, then which of the following is/are correct?
1. x 2 + y 2 varies as x 2 - y 2
2. \(\frac{x}{y^2}\) varies inversely as y
3. \(\sqrt[n]{x^2y}\) varies as \(\sqrt[2n]{x^4y^2}\)Select the correct answer using the code given below:
What is the square root of \(15 - 4\sqrt {14} \) ?
What is \(\sqrt {\frac{{0.064{\rm{\;}} \times {\rm{\;}}6.25}}{{0.081{\rm{\;}} \times {\rm{\;}}4.84}}} {\rm{\;}}\) equal to?
What is the square root of \(\frac{{{{\left( {0.35} \right)}^2} + {\rm{\;}}0.70{\rm{\;}} + {\rm{\;}}1}}{{2.25}} + 0.19{\rm{\;}}?\)
If one root of (a 2– 5a + 3)x 2+ (3a – 1)x + 2 = 0 is twice the other, then what is the value of ‘a’?
What is the value of \(\frac{{{{\left( {443{\rm{\;}} + {\rm{\;}}547} \right)}^2} + {\rm{\;}}{{\left( {443{\rm{\;}} - {\rm{\;}}547} \right)}^2}{\rm{\;}}}}{{443{\rm{\;}} \times {\rm{\;}}443{\rm{\;}} + {\rm{\;}}547{\rm{\;}} \times {\rm{\;}}547}}\) ?
What is the value of [(√5 - √3) / (√5 + √3)] - [(√5 + √3) / (√5 - √3)]?
Which one of the following is the largest number among 2222 2, 222 22 , 22 222 , 2 2222 ?
If x = 2 + 2 2/3 + 2 1/3 , then the value of the expression x 3- 6x 2+ 6x will be
Important Questions from Surds and Indices
The cube root of - 64 × - 1331 is:
If (27) m = (81) n, then m 2: mn = ?
if 49 n + 49 n + 49 n + 49 n + 49 n + 49 n + 49 n = 7 2221 , then n = ?
If a x= b y= c zand b 2= ac then y =
The value of (0.3) [{(200 - 146)/(3 × 3 × 3)} - 3] is:
