If \(x = \sqrt{225} + \sqrt{484}\), what is the value of \(x^2 - \left[(\sqrt{225})^2 + (32)^2\right]\)?
120
First, evaluate the square roots: \(\sqrt{225} = 15\) and \(\sqrt{484} = 22\).
So \(x = 15 + 22 = 37\).
Calculate \(x^2 = 37^2 = 1369\).
Calculate the bracket: \((\sqrt{225})^2 + (32)^2 = 225 + 1024 = 1249\).
Therefore, \(x^2 - \left[(\sqrt{225})^2 + (32)^2\right] = 1369 - 1249 = 120\).
Hence, the value of the expression is 120.
Similar Questions
- Given that $7^{0.07} = x$, $7^{0.07} = y$ and $x^z = y^3$, then the value of z is close to:
- Given that $76^{0.44} = x$, $76^{0.93} = y$ and $x^z = y^3$, then the value of z is close to:
- Find the value of $57^{-8} \div 57^{17} \times 57^{-18}$.
- Find the value of: $93^{-6} \div 93^{16} \times 93^{-12}$
- The square root of $\frac{(3\frac{1}{4})^{4} - (4\frac{1}{3})^{4}}{(3\frac{1}{4})^{2} - (4\frac{1}{3})^{2}}$ is:
- Simplify: $(1^3 + 2^3 + 3^3 + \dots + 8^3)^{\frac{-5}{2}}$
- If $\sqrt{54} + \sqrt{150} = 19.60$, then what will the value of $\sqrt{216} + \sqrt{96}$ be? Give your answer, correct to one decimal place.
- Solve the following:
$(625)^{0.17} \times (625)^{0.08} = ?$ - If $\frac{9^m \times 3^5 \times 27^3}{3 \times 81^4} = 3^9$, then the value of m is:
- If $\sqrt{45} + \sqrt{125} = 17.88$ then what will be the value of $\sqrt{180} + \sqrt{80}$ ?
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:
\(\sqrt{46.24}+\sqrt{0.4624}+\sqrt{0.004624}\)
