The value of $\sqrt{{91}+\sqrt{70+\sqrt121}}$ is-

Q: The value of $\sqrt{{91}+\sqrt{70+\sqrt121}}$ is-

To determine the value of $\sqrt{91+\sqrt{70+\sqrt{121}}}$, we need to evaluate the expression step by step. 1. **Evaluate the innermost square root:** \[ \sqrt{121} = 11 \] 2. **Substitute and evaluate the next square root:** \[ \sqrt{70 + \sqrt{121}} = \sqrt{70 + 11} = \sqrt{81} \] \[ \sqrt{81} = 9 \] 3. **Substitute and evaluate the outermost square root:** \[ \sqrt{91 + \sqrt{70 + \sqrt{121}}} = \sqrt{91 + 9} = \sqrt{100} \] \[ \sqrt{100} = 10 \] Thus, the value of the expression $\sqrt{91+\sqrt{70+\sqrt{121}}}$ is 10, which corresponds to Option 2. **Explanation for why each option is incorrect:** - **Option 1 (9):** This option is incorrect because the final evaluation of the expression results in $\sqrt{100}$, which is 10, not 9. - **Option 3 (11):** This option is incorrect because the calculation of $\sqrt{100}$ results in 10, not 11. - **Option 4 (12):** This option is incorrect because the square root of 100 is 10, not 12. Therefore, the correct answer is indeed Option 2, which is 10.

Question

Accepted Answer

To determine the value of $\sqrt{91+\sqrt{70+\sqrt{121}}}$, we need to evaluate the expression step by step.

1. **Evaluate the innermost square root:**
   $$
   \sqrt{121} = 11
   $$

2. **Substitute and evaluate the next square root:**
   $$
   \sqrt{70 + \sqrt{121}} = \sqrt{70 + 11} = \sqrt{81}
   $$
   $$
   \sqrt{81} = 9
   $$

3. **Substitute and evaluate the outermost square root:**
   $$
   \sqrt{91 + \sqrt{70 + \sqrt{121}}} = \sqrt{91 + 9} = \sqrt{100}
   $$
   $$
   \sqrt{100} = 10
   $$

Thus, the value of the expression $\sqrt{91+\sqrt{70+\sqrt{121}}}$ is 10, which corresponds to Option 2.

**Explanation for why each option is incorrect:**

- **Option 1 (9):** This option is incorrect because the final evaluation of the expression results in $\sqrt{100}$, which is 10, not 9.

- **Option 3 (11):** This option is incorrect because the calculation of $\sqrt{100}$ results in 10, not 11.

- **Option 4 (12):** This option is incorrect because the square root of 100 is 10, not 12.

Therefore, the correct answer is indeed Option 2, which is 10.