$\sqrt{0.01 + \sqrt{0.0064}}$ is equal to :

Q: $\sqrt{0.01 + \sqrt{0.0064}}$ is equal to :

To solve the expression $\sqrt{0.01 + \sqrt{0.0064}}$, we need to evaluate each part step by step and verify why Option 2 is the correct answer. 1. **Evaluate $\sqrt{0.0064}$:** \[ \sqrt{0.0064} = 0.08 \] This is because $0.08 \times 0.08 = 0.0064$. 2. **Add 0.01 to the result:** \[ 0.01 + 0.08 = 0.09 \] 3. **Evaluate $\sqrt{0.09}$:** \[ \sqrt{0.09} = 0.3 \] This is because $0.3 \times 0.3 = 0.09$. Therefore, the expression $\sqrt{0.01 + \sqrt{0.0064}}$ simplifies to 0.3, which corresponds to Option 2. **Explanation of why other options are incorrect:** - **Option 1: 0.03** This option is incorrect because $\sqrt{0.09} = 0.3$, not 0.03. The calculation of $\sqrt{0.09}$ clearly results in 0.3. - **Option 3: $0.3\sqrt{2}$** This option is incorrect because the expression $\sqrt{0.01 + \sqrt{0.0064}}$ simplifies to a single real number, 0.3, not a multiple of $\sqrt{2}$. - **Option 4: 3** This option is incorrect because 3 is much larger than the calculated value of 0.3. The square root of 0.09 is 0.3, not 3. In conclusion, the correct answer is Option 2, which is 0.3, as demonstrated by the step-by-step evaluation of the expression.

Question

Accepted Answer

To solve the expression $\sqrt{0.01 + \sqrt{0.0064}}$, we need to evaluate each part step by step and verify why Option 2 is the correct answer.

1. **Evaluate $\sqrt{0.0064}$:**

$$
   \sqrt{0.0064} = 0.08
   $$

This is because $0.08 \times 0.08 = 0.0064$.

2. **Add 0.01 to the result:**

$$
   0.01 + 0.08 = 0.09
   $$

3. **Evaluate $\sqrt{0.09}$:**

$$
   \sqrt{0.09} = 0.3
   $$

This is because $0.3 \times 0.3 = 0.09$.

Therefore, the expression $\sqrt{0.01 + \sqrt{0.0064}}$ simplifies to 0.3, which corresponds to Option 2.

**Explanation of why other options are incorrect:**

- **Option 1: 0.03**

This option is incorrect because $\sqrt{0.09} = 0.3$, not 0.03. The calculation of $\sqrt{0.09}$ clearly results in 0.3.

- **Option 3: $0.3\sqrt{2}$**

This option is incorrect because the expression $\sqrt{0.01 + \sqrt{0.0064}}$ simplifies to a single real number, 0.3, not a multiple of $\sqrt{2}$.

- **Option 4: 3**

This option is incorrect because 3 is much larger than the calculated value of 0.3. The square root of 0.09 is 0.3, not 3.

In conclusion, the correct answer is Option 2, which is 0.3, as demonstrated by the step-by-step evaluation of the expression.