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What approximate value will come in plac...

What approximate value will come in place of questions mark (?) in the following questions?
`sqrt(3949)xxsqrt(1220)-:sqrt(280)=?`

A

120

B

130

C

140

D

150

Text Solution

AI Generated Solution

The correct Answer is:
To solve the expression \( \sqrt{3949} \times \sqrt{1220} \div \sqrt{280} = ? \), we can follow these steps: ### Step 1: Approximate \( \sqrt{3949} \) To find \( \sqrt{3949} \), we look for perfect squares near 3949. The perfect square closest to 3949 is \( 63^2 = 3969 \). Thus, we can approximate: \[ \sqrt{3949} \approx 63 \] ### Step 2: Approximate \( \sqrt{1220} \) Next, we approximate \( \sqrt{1220} \). The perfect square closest to 1220 is \( 35^2 = 1225 \). Therefore, we can approximate: \[ \sqrt{1220} \approx 35 \] ### Step 3: Approximate \( \sqrt{280} \) Now, we find \( \sqrt{280} \). The perfect square closest to 280 is \( 17^2 = 289 \). Thus, we can approximate: \[ \sqrt{280} \approx 17 \] ### Step 4: Substitute the approximations into the expression Now we substitute the approximated values back into the expression: \[ \sqrt{3949} \times \sqrt{1220} \div \sqrt{280} \approx 63 \times 35 \div 17 \] ### Step 5: Calculate the multiplication and division First, calculate \( 63 \times 35 \): \[ 63 \times 35 = 2205 \] Now divide by 17: \[ 2205 \div 17 \approx 129.12 \] ### Step 6: Round to the nearest whole number Since we are looking for an approximate value, we can round 129.12 to: \[ ? \approx 129 \] ### Final Answer The approximate value that comes in place of the question mark (?) is: \[ \boxed{129} \]
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