Simplifying the Square Root Expression
The question asks to simplify the expression \((\sqrt{3} + \sqrt{2})^2\). We can solve this using the algebraic identity for the square of a sum: \( (a + b)^2 = a^2 + 2ab + b^2 \)
Applying the Binomial Square Formula
Let \(a = \sqrt{3}\) and \(b = \sqrt{2}\). Substitute these values into the identity:
- First term squared: \( a^2 = (\sqrt{3})^2 = 3 \)
- Twice the product of the terms: \( 2ab = 2 \times \sqrt{3} \times \sqrt{2} = 2\sqrt{3 \times 2} = 2\sqrt{6} \)
- Second term squared: \( b^2 = (\sqrt{2})^2 = 2 \)
Final Simplification
Add the results obtained:
\( (\sqrt{3} + \sqrt{2})^2 = 3 + 2\sqrt{6} + 2 \)
Combine the constant terms:
\( (3 + 2) + 2\sqrt{6} = 5 + 2\sqrt{6} \)
The simplified form of the expression is \(5 + 2\sqrt{6}\).
Similar Questions
- If $x = 2 + \sqrt{3}$, find $x - \frac{1}{x}$.
- Simplify:
$\sqrt{12} + \sqrt{75}$ - What will come in place of ? to satisfy the equation : $(\sqrt{6}-1)^2 = ? - 2\sqrt{6}$
- 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 $x^2 - 2$.
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:
\(\sqrt{46.24}+\sqrt{0.4624}+\sqrt{0.004624}\)
