Question

which equations are true? select two answers a. \\(\sqrt{16} = \pm 8\\) b. \\(\sqrt3{64} = 4\\) c. \\(\sqrt{144} = \pm 12\\) d. \\(\sqrt3{216} = 72\\) \\(\sqrt{900} = 30\\)

Explanation:

Step1: Analyze Option A

The square root of a non - negative number, by definition, gives the non - negative square root (the principal square root). So, $\sqrt{16}$ is the principal square root of 16, and since $4^2 = 16$, $\sqrt{16}=4$, not $\pm8$. So option A is false.

Step2: Analyze Option B

For the cube root, if we want to find $\sqrt[3]{64}$, we need to find a number $x$ such that $x^3=64$. We know that $4^3 = 4\times4\times4=64$, so $\sqrt[3]{64} = 4$. Option B is true.

Step3: Analyze Option C

The principal square root of 144, $\sqrt{144}$, is the non - negative number whose square is 144. Since $12^2=144$, $\sqrt{144} = 12$ (not $\pm12$; the equation $x^2 = 144$ has solutions $x=\pm12$, but the square root function $\sqrt{x}$ for $x\geq0$ gives the non - negative root). So option C is false.

Step4: Analyze Option D

To find $\sqrt[3]{216}$, we need a number $x$ such that $x^3 = 216$. We know that $6^3=6\times6\times6 = 216$, so $\sqrt[3]{216}=6
eq72$. Option D is false.

Step5: Analyze Option E

For the square root of 900, $\sqrt{900}$ is the non - negative number whose square is 900. Since $30^2 = 900$, $\sqrt{900}=30$. Option E is true. But wait, the problem says "Select two answers". Wait, maybe there is a typo in the option E (maybe it's $\sqrt{900}=30$). Wait, let's re - check. Wait, the options are A: $\sqrt{16}=\pm8$, B: $\sqrt[3]{64}=4$, C: $\sqrt{144}=\pm12$, D: $\sqrt[3]{216}=72$, E: $\sqrt{900}=30$. So B is true, and E is true? Wait, but the original problem says "Select two answers". Wait, maybe I misread. Wait, let's check again. Wait, the cube root of 64: $4^3 = 64$, so B is correct. The square root of 900: $30^2=900$, so E is correct. But maybe the user made a typo in the option E (maybe it's $\sqrt{900}=30$). So the correct options are B and E? Wait, but in the given options, let's check again. Wait, the options are:

A. $\sqrt{16}=\pm8$

B. $\sqrt[3]{64}=4$

C. $\sqrt{144}=\pm12$

D. $\sqrt[3]{216}=72$

E. $\sqrt{900}=30$

So B is correct ($\sqrt[3]{64}=4$) and E is correct ($\sqrt{900}=30$). But maybe the problem expects B and E? Wait, but let's check the original problem again. Wait, maybe the option E is $\sqrt{900}=30$. So the two correct options are B and E? Wait, but in the keyboard, the options are C, B, D, E, A. Wait, maybe there is a mistake in my earlier analysis. Wait, no:

• B: $\sqrt[3]{64}=4$ (correct, since $4^3 = 64$)

• E: $\sqrt{900}=30$ (correct, since $30^2=900$)

But the problem says "Select two answers". So the two correct options are B and E? Wait, but maybe the option E was written as $\sqrt{900}=30$. So the correct options are B. $\sqrt[3]{64}=4$ and E. $\sqrt{900}=30$. But let's check the original problem again. Wait, the user's image shows options:

A. $\sqrt{16}=\pm8$

B. $\sqrt[3]{64}=4$

C. $\sqrt{144}=\pm12$

D. $\sqrt[3]{216}=72$

E. $\sqrt{900}=30$

So the correct options are B and E? Wait, but maybe I made a mistake. Wait, no:

• B: $\sqrt[3]{64}=4$ (correct)

• E: $\sqrt{900}=30$ (correct)

But the problem says "Select two answers". So the two correct options are B and E. But let's check again:

For option B: $\sqrt[3]{64}$. Since $4\times4\times4 = 64$, so $\sqrt[3]{64}=4$. Correct.

For option E: $\sqrt{900}$. Since $30\times30 = 900$, so $\sqrt{900}=30$. Correct.

Wait, but maybe the problem has a typo and E is $\sqrt{900}=30$. So the two correct options are B and E. But in the keyboard, the options are C, B, D, E, A. So the correct options are B. $\sqrt[3]{64}=4$ and E. $\sqrt{900}=30$.

Answer:

B. $\sqrt[3]{64}=4$, E. $\sqrt{900}=30$