Expand the Equation
The problem requires finding the value that satisfies the equation: $ (\sqrt{6}-1)^2 = ? - 2\sqrt{6} $ First, expand the left side, $ (\sqrt{6}-1)^2 $, using the algebraic identity $ (a-b)^2 = a^2 - 2ab + b^2 $. Here, $ a = \sqrt{6} $ and $ b = 1 $. $ (\sqrt{6}-1)^2 = (\sqrt{6})^2 - 2(\sqrt{6})(1) + (1)^2 $ $ (\sqrt{6}-1)^2 = 6 - 2\sqrt{6} + 1 $ $ (\sqrt{6}-1)^2 = 7 - 2\sqrt{6} $
Solve for the Unknown
Now, substitute the expanded form back into the original equation: $ 7 - 2\sqrt{6} = ? - 2\sqrt{6} $ To isolate the question mark (?), add $ 2\sqrt{6} $ to both sides of the equation: $ 7 - 2\sqrt{6} + 2\sqrt{6} = ? - 2\sqrt{6} + 2\sqrt{6} $ $ 7 = ? $ Thus, the value that comes in place of ? is 7.
Similar Questions
If \(x = \sqrt{\dfrac{2 + \sqrt{3}}{2 - \sqrt{3}}}\), determine the value of \(x^2 + x - 9\).
Evaluate: \(\sqrt{12 + \sqrt{12 + \sqrt{12 + \cdots}}}\)
- If $x = 2 + \sqrt{3}$, find $x - \frac{1}{x}$.
- The value of $\sqrt{11 - 2\sqrt{30}} - \frac{1}{\sqrt{11 - 2\sqrt{30}}}$ is:
- Simplify:
$\frac{\sqrt{5+2\sqrt{6}}}{\sqrt{5-2\sqrt{6}}}$ Find the value of \(\sqrt{388 + \sqrt{127 + \sqrt{289}}}\).
Simplify the expression: \(\sqrt{9 + 4\sqrt{5}}\)
Choose the correct relation:
(i) \(\sqrt{10} < 3.2\)
(ii) \(\sqrt{11} < \sqrt{12}\)
(iii) \(\sqrt{13} < \sqrt{14}\)
Simplify:
\(\dfrac{1}{\sqrt{7}-\sqrt{3}} + \dfrac{1}{\sqrt{7}+\sqrt{3}}\)
If \(\sqrt{a} + \sqrt{b} = 5\) and \(\sqrt{a} - \sqrt{b} = 1\), what are the values of a and b?
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:
