Round to the nearest integer. $$ \begin{array}{ll} ext { (1) } \sqrt{30} & ext { (2) } \sqrt{80} \ ext { (3) } \sqrt[3]{100} & ext { (4) } \sqrt[3]{30}\end{array} $$

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Round to the nearest integer. $$ \begin{array}{ll}	ext { (1) } \sqrt{30} & 	ext { (2) } \sqrt{80} \ 	ext { (3) } \sqrt[3]{100} & 	ext { (4) } \sqrt[3]{30}\end{array} $$

UpStudy AI · Accepted Answer

1. For $$\sqrt{30}$$:
   - We know that $$5^2=25$$ and $$6^2=36$$, so $$\sqrt{30}$$ is between 5 and 6.
   - In fact, $$\sqrt{30} \approx 5.477$$.
   - Rounding to the nearest integer gives **5**.

2. For $$\sqrt{80}$$:
   - Notice that $$ \sqrt{80}=\sqrt{16 	imes 5}=4\sqrt{5}$$.
   - Since $$\sqrt{5} \approx 2.236$$, we have $$\sqrt{80} \approx 4 	imes 2.236 \approx 8.944$$.
   - Rounding to the nearest integer gives **9**.

3. For $$\sqrt[3]{100}$$:
   - We know that $$4^3=64$$ and $$5^3=125$$, so $$\sqrt[3]{100}$$ lies between 4 and 5.
   - More precisely, $$\sqrt[3]{100} \approx 4.642$$.
   - Rounding to the nearest integer gives **5**.

4. For $$\sqrt[3]{30}$$:
   - We note that $$3^3=27$$ and $$4^3=64$$, so $$\sqrt[3]{30}$$ is between 3 and 4.
   - In fact, $$\sqrt[3]{30} \approx 3.107$$.
   - Rounding to the nearest integer gives **3**.

Thus, the rounded answers are:  
(1) $$5$$, (2) $$9$$, (3) $$5$$, (4) $$3$$.
The rounded answers are: 1. 5 2. 9 3. 5 4. 3

Round to the nearest integer.

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