Question

question 12
0/1 pt 100 99 details
use a calculator to approximate the following square root to the nearest thousandth.
a. $sqrt{28}+sqrt{175}=$
b. $sqrt{203}=$
c. $2sqrt{7}+5sqrt{7}=$
d. $7sqrt{7}=$
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Explanation:

Step1: Simplify and compute a

First, simplify radicals: $\sqrt{28}=2\sqrt{7}$, $\sqrt{175}=5\sqrt{7}$. Sum: $2\sqrt{7}+5\sqrt{7}=7\sqrt{7}$. Calculate $7\sqrt{7}\approx7\times2.6458=18.5206$

Step2: Compute b directly

Calculate $\sqrt{203}\approx14.2478$

Step3: Combine like radicals for c

Add coefficients: $2\sqrt{7}+5\sqrt{7}=(2+5)\sqrt{7}=7\sqrt{7}\approx18.5206$

Step4: Compute d directly

Calculate $7\sqrt{7}\approx7\times2.6458=18.5206$

Answer:

a. $18.521$
b. $14.248$
c. $18.521$
d. $18.521$