Radical Simplification: Initial Expression
First, simplify the given expression \( \sqrt{45} + \sqrt{125} \).
- \( \sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5} \)
- \( \sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5} \)
- Sum: \( 3\sqrt{5} + 5\sqrt{5} = 8\sqrt{5} \).
Radical Value: \( \sqrt{5} \) Determination
We are given that \( \sqrt{45} + \sqrt{125} = 17.88 \), which simplifies to \( 8\sqrt{5} = 17.88 \).
Calculate the value of \( \sqrt{5} \):
\( \sqrt{5} = \frac{17.88}{8} = 2.235 \)
Radical Simplification: Target Expression
Now, simplify the expression whose value needs to be found: \( \sqrt{180} + \sqrt{80} \).
- \( \sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5} \)
- \( \sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5} \)
- Sum: \( 6\sqrt{5} + 4\sqrt{5} = 10\sqrt{5} \).
Final Value Calculation
Substitute the calculated value of \( \sqrt{5} \) into the target expression \( 10\sqrt{5} \):
\( 10\sqrt{5} = 10 \times 2.235 \)
\( 10\sqrt{5} = 22.35 \).
Alternatively, use the given value relation directly:
Since \( 8\sqrt{5} \) corresponds to \( 17.88 \), then \( 10\sqrt{5} \) corresponds to \( \frac{10}{8} \times 17.88 \).
\( \frac{10}{8} \times 17.88 = \frac{5}{4} \times 17.88 = 5 \times 4.47 = 22.35 \).
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:
- $\frac{225^{0.2} \times 225^{0.3}}{225^{0.6} \times 225^{0.4}}$ is equal to:
Important Questions from Surds and Indices
The value of (0.3) [{(200 - 146)/(3 × 3 × 3)} - 3] is:
The expression \(\frac{{15\left( {\sqrt {10} + \sqrt 5 } \right)}}{{\sqrt {10\;} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}\) is equal to:
Let \(x = \left( {\frac{{√ {1875} }}{{√ {3888} }} \div \frac{{√ {1200} }}{{\sqrt 768}}} \right) \times \frac{{√ {175} }}{{√ {1792} }}\) . Then √x is equal to:
If \(x = \sqrt {-\sqrt 3 + \sqrt {3 + 8\sqrt {7 + 4\sqrt 3}}}\) where x > 0, then the value of x is equal to:
What is the value of \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}−\sqrt{5}} \div \frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}−\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}\) ?
