Solve (8)^(2)+sqrt((3)^(2)sqrt((6)^(2)sqrt((9)^(2)))) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$${ 8 }^{ 2 } + \sqrt{ { 3 }^{ 2 } \sqrt{ { 6 }^{ 2 } \sqrt{ { 9 }^{ 2 } } } }$$

Evaluate

$9\sqrt{2}+64\approx 76.727922061$

Solution Steps

Calculate $8$ to the power of $2$ and get $64$.

$$64+\sqrt{3^{2}\sqrt{6^{2}\sqrt{9^{2}}}}$$

Calculate $3$ to the power of $2$ and get $9$.

$$64+\sqrt{9\sqrt{6^{2}\sqrt{9^{2}}}}$$

Calculate $6$ to the power of $2$ and get $36$.

$$64+\sqrt{9\sqrt{36\sqrt{9^{2}}}}$$

Calculate $9$ to the power of $2$ and get $81$.

$$64+\sqrt{9\sqrt{36\sqrt{81}}}$$

Calculate the square root of $81$ and get $9$.

$$64+\sqrt{9\sqrt{36\times 9}}$$

Multiply $36$ and $9$ to get $324$.

$$64+\sqrt{9\sqrt{324}}$$

Calculate the square root of $324$ and get $18$.

$$64+\sqrt{9\times 18}$$

Multiply $9$ and $18$ to get $162$.

$$64+\sqrt{162}$$

Factor $162=9^{2}\times 2$. Rewrite the square root of the product $\sqrt{9^{2}\times 2}$ as the product of square roots $\sqrt{9^{2}}\sqrt{2}$. Take the square root of $9^{2}$.

$$64+9\sqrt{2}$$