$\sqrt{3}(\sqrt{12} - \sqrt{27})$
Simplify Radical Expression: $\\sqrt{3}(\sqrt{12} - \sqrt{27})$
The goal is to simplify the given mathematical expression involving square roots.
Step 1: Simplify Terms Inside Parentheses
First, simplify the square roots $\sqrt{12}$ and $\sqrt{27}$:
- $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$
- $\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}$
Step 2: Substitute Simplified Terms
Substitute these simplified forms back into the original expression:
$\sqrt{3}(2\sqrt{3} - 3\sqrt{3})$
Step 3: Combine Like Terms
Combine the terms inside the parentheses:
$2\sqrt{3} - 3\sqrt{3} = (2-3)\sqrt{3} = -1\sqrt{3} = -\sqrt{3}$
Step 4: Final Calculation
Now, multiply the term outside the parentheses by the simplified term inside:
$\sqrt{3} \times (-\sqrt{3})$
This simplifies to:
$-\sqrt{3} \times \sqrt{3} = -(\sqrt{3})^2 = -3$
The simplified value of the expression is -3.
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 $x^2 - 2$.
- Simplify: $(\sqrt{3} + \sqrt{2})^2$
Rationalize:
$\frac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}}$- 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:
\(\sqrt{46.24}+\sqrt{0.4624}+\sqrt{0.004624}\)
