Evaluating the Square Root Expression
To find the value of the given expression, we need to simplify the fraction inside the square root first.
The expression is:
$ \sqrt{\frac{1.21 \times 0.9}{1.1 \times 0.11}} $
Step-by-Step Simplification
- Rewrite the terms to identify common factors. Notice that $1.21 = 1.1 \times 1.1$.
- Substitute this into the expression: $ \sqrt{\frac{(1.1 \times 1.1) \times 0.9}{1.1 \times 0.11}} $
- Cancel out one factor of $1.1$ from the numerator and the denominator: $ \sqrt{\frac{1.1 \times 0.9}{0.11}} $
- Now, simplify the remaining terms. We can rewrite $1.1$ as $11 \times 0.1$ and $0.11$ as $11 \times 0.01$: $ \sqrt{\frac{(11 \times 0.1) \times 0.9}{11 \times 0.01}} $
- Cancel out the factor of $11$: $ \sqrt{\frac{0.1 \times 0.9}{0.01}} $
- Calculate the product in the numerator: $0.1 \times 0.9 = 0.09$. $ \sqrt{\frac{0.09}{0.01}} $
- Divide the numbers inside the square root: $\frac{0.09}{0.01} = 9$. $ \sqrt{9} $
- Calculate the final square root: $ \sqrt{9} = 3 $
The value of the expression is 3.
Similar Questions
What will the value of the following expression be?
$\left(\frac{6+3}{3}\right) - 5 \times (4+5)$
- What is the value of the following expression?
$\frac{\sqrt{225}}{14} \times \frac{\sqrt{196}}{22} \times \frac{\sqrt{484}}{15}$ - The value of $\frac{(5.4)^3 - 0.064}{(5.4)^2 + 2.16 + 0.16}$ is:
- The value of $\sqrt{10 + \sqrt{221 + \sqrt{12 + \sqrt{16}}}}$ is:
- Solve the following.
$(1 + \frac{1}{x})(1 + \frac{1}{x+1})(1 + \frac{1}{x+2})(1 + \frac{1}{x+3}) = ?$ - The value of $\sqrt{0.04} + \sqrt{1.44} + \sqrt{1.69} + \sqrt{0.0009}$ is:
- The value of $\sqrt{196} + \sqrt{0.0361} - \sqrt{7.29}$ is ____.
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Important Questions from Simplification
What will come in the place of the question mark ‘?’ in the following question?
(15 + 24) × 3 ÷ 13 + 18 – 5 = ?
What should come in place of the question mark '?' in the following question?
\n13 × 3 of 5 ÷ 26 = ? + 2.5What should come in place of the question mark '?' in the following question?
10% of 450 - (8 × 5) = ? × 5
What will come in the place of the question mark ‘?’ in the following question?
(66)2 - (34)2 + ?2 = (60)2
What will come in the place of the question mark ‘?’ in the following question?
3 × ? ÷ 9 = ∛729 × √121
