which is the best estimate of $sqrt{0.96}$ to the nearest hundredth?\n0.96\n0.97\n0.98\n1.00
which is the best estimate of $sqrt{0.96}$ to the nearest hundredth?\n0.96\n0.97\n0.98\n1.00
Answer
Explanation:
Step1: Recall square - root property
We know that if (x = \sqrt{a}), then (x^{2}=a). We need to find which number squared is closest to (0.96).
Step2: Square each option
- For (0.96), (0.96^{2}=0.96\times0.96 = 0.9216).
- For (0.97), (0.97^{2}=0.97\times0.97=0.9409).
- For (0.98), (0.98^{2}=0.98\times0.98 = 0.9604).
- For (1.00), (1.00^{2}=1.00\times1.00 = 1.00).
Step3: Compare the results
We want the number whose square is closest to (0.96). The differences are:
- (|0.96 - 0.9216|=0.0384).
- (|0.96 - 0.9409|=0.0191).
- (|0.96 - 0.9604|=0.0004).
- (|0.96 - 1.00|=0.04). The smallest difference is (0.0004) when the number is (0.98).
Answer:
C. (0.98)