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:
- Find the value of $57^{-8} \div 57^{17} \times 57^{-18}$.
- If $\sqrt{45} + \sqrt{125} = 17.89$, then what will be the value of $\sqrt{180} + \sqrt{80}$?
(Give your answer to one decimal place.) - What is the value of $\frac{4+\sqrt{2}}{\sqrt{2}+1}$?
If $\sqrt{2916} = 54$ then what is the value of the following?
$\sqrt{29.16} + \sqrt{0.2916} + \sqrt{0.002916} + \sqrt{0.00002916}$
- Find the value of $95^{-17} \div 95^{9} \times 95^{-15}$.
- $(\sqrt{5} + \sqrt{11})(\sqrt{5} - \sqrt{11})$ is equal to:
- What is the value of $\sqrt{75} + \sqrt{147}$?
- Find $\sqrt{\frac{1521}{1849}}$
If $\frac{2\sqrt{2}+\sqrt{7}}{2\sqrt{2}-\sqrt{7}} = x + y\sqrt{14}$, find the value of y.
Important Questions from Surds and Indices
Find the cube root of 78402752
Find the value of :
[(3 × 3 × 3 × 3 × 3 × 3) 6 ÷ (3 × 3 × 3 × 3) 7 × 3 4]
The cube root of - 64 × - 1331 is:
If (27) m = (81) n, then m 2: mn = ?
if 49 n + 49 n + 49 n + 49 n + 49 n + 49 n + 49 n = 7 2221 , then n = ?
