Answer:
Factor 12=2^{2}\times 312=2
2
×3. Rewrite the square root of the product \sqrt{2^{2}\times 3}
2
2
×3
as the product of square roots \sqrt{2^{2}}\sqrt{3}
2
2
3
. Take the square root of 2^{2}2
2
.
3\times 2\sqrt{3}+\sqrt{75}3×2
3
+
75
Step 2
Multiply 33 and 22 to get 66.
6\sqrt{3}+\sqrt{75}6
3
+
75
Hint
Multiply two factors together.
Step 3
Factor 75=5^{2}\times 375=5
2
×3. Rewrite the square root of the product \sqrt{5^{2}\times 3}
5
2
×3
as the product of square roots \sqrt{5^{2}}\sqrt{3}
5
2
3
. Take the square root of 5^{2}5
2
.
6\sqrt{3}+5\sqrt{3}6
3
+5
3
Step 4
Combine 6\sqrt{3}6
3
and 5\sqrt{3}5
3
to get 11\sqrt{3}11
3
.
11\sqrt{3}11
3
Hint
Combine like terms.
Solution
11\sqrt{3}\approx 19.05255888311
3
≈19.052558883
