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 $x = 2 + \sqrt{3}$, find $x - \frac{1}{x}$.
- Simplify:
$\sqrt{12} + \sqrt{75}$ - Simplify:
$\frac{\sqrt{5+2\sqrt{6}}}{\sqrt{5-2\sqrt{6}}}$ - The value of $\sqrt{11 - 2\sqrt{30}} - \frac{1}{\sqrt{11 - 2\sqrt{30}}}$ is:
- If $x = \sqrt{2} + 1$, find $x^2 - 2$.
- Simplify: $(\sqrt{3} + \sqrt{2})^2$
Rationalize:
$\frac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}}$- Simplify:
$\sqrt{3}(\sqrt{12} - \sqrt{27})$ - Simplify:
$\frac{\sqrt{5+2\sqrt{6}} + \sqrt{5-2\sqrt{6}}}{\sqrt{2}}$ Simplify: \(\sqrt{7+4\sqrt{3}}\)
Important Questions from Surds and Indices
The value of \(\frac{{{{\left( {251} \right)}^3} + {{\left( {249} \right)}^3}}}{{25.1 \times 25.1 - 624.99 + 24.9 \times 24.9}}\) is 5 × 10 k , where the value of k is :
Find the value of m in \(\left(\frac{2}{7}\right)^{-3} \times \left(\frac{2}{7}\right)^{-5}=\left (\frac{2}{7}\right)^{-3m+1}\)
If √625 = 25; then√(.00000625/25)is:
A. 0.0025
B. 0.001
C. 0.0001
D. 0.0005Find the value of:
\(\sqrt{150}-\sqrt{54}-\sqrt{24}\)
If \(\sqrt{4624}=68\) , then the value of:
\(\sqrt{46.24}+\sqrt{0.4624}+\sqrt{0.004624}\)
