What is the square root of 37,221,835 to four decimal places?

What is the square root of 37,221,835 to four decimal places?

• A. 60.0097
• B. 61.0098
• C. 61.1000
• D. 61.0097

Answer: (D)

When you’re finding a square root to four decimals for a large number, start by locating the integer part with nearby squares. Here, 6100 squared is 37,210,000, which is just under 37,221,835, so the root is slightly more than 6100. A quick refinement uses Newton’s method. Take an initial guess of 6100. Divide the target by that guess to get N/g0. Since 37,221,835 divided by 6100 is about 6101.9402, the next approximation is the average of 6100 and 6101.9402, which is about 6100.9701. A further refinement brings it to roughly 6100.9700. So, to four decimal places, the square root is about 6100.9700. The options shown appear to miss a zero (they’re around 61), which is why none match the correct result.

When you’re finding a square root to four decimals for a large number, start by locating the integer part with nearby squares. Here, 6100 squared is 37,210,000, which is just under 37,221,835, so the root is slightly more than 6100.

A quick refinement uses Newton’s method. Take an initial guess of 6100. Divide the target by that guess to get N/g0. Since 37,221,835 divided by 6100 is about 6101.9402, the next approximation is the average of 6100 and 6101.9402, which is about 6100.9701. A further refinement brings it to roughly 6100.9700.

So, to four decimal places, the square root is about 6100.9700. The options shown appear to miss a zero (they’re around 61), which is why none match the correct result.