Solve (2)^(2)\times(5)^(2)\times(9)^(2)sqrt(6\times(1)^(2)(2)^(2)(3)^(2)(4)^(2)(5)^(2)(6)^(2)(7)^(2)(8)^(2)(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

$${ 2 }^{ 2 } \times { 5 }^{ 2 } \times { 9 }^{ 2 } \sqrt{ 6 \times { 1 }^{ 2 } { 2 }^{ 2 } { 3 }^{ 2 } { 4 }^{ 2 } { 5 }^{ 2 } { 6 }^{ 2 } { 7 }^{ 2 } { 8 }^{ 2 } { 9 }^{ 2 } }$$

Evaluate

$2939328000\sqrt{6}\approx 7199853786.675393105$

Solution Steps

To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.

$$2^{2}\times 5^{2}\times 9^{2}\sqrt{6^{3}\times 1^{2}\times 2^{2}\times 3^{2}\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Calculate $2$ to the power of $2$ and get $4$.

$$4\times 5^{2}\times 9^{2}\sqrt{6^{3}\times 1^{2}\times 2^{2}\times 3^{2}\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Calculate $5$ to the power of $2$ and get $25$.

$$4\times 25\times 9^{2}\sqrt{6^{3}\times 1^{2}\times 2^{2}\times 3^{2}\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Multiply $4$ and $25$ to get $100$.

$$100\times 9^{2}\sqrt{6^{3}\times 1^{2}\times 2^{2}\times 3^{2}\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

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

$$100\times 81\sqrt{6^{3}\times 1^{2}\times 2^{2}\times 3^{2}\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Multiply $100$ and $81$ to get $8100$.

$$8100\sqrt{6^{3}\times 1^{2}\times 2^{2}\times 3^{2}\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Calculate $6$ to the power of $3$ and get $216$.

$$8100\sqrt{216\times 1^{2}\times 2^{2}\times 3^{2}\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Calculate $1$ to the power of $2$ and get $1$.

$$8100\sqrt{216\times 1\times 2^{2}\times 3^{2}\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Multiply $216$ and $1$ to get $216$.

$$8100\sqrt{216\times 2^{2}\times 3^{2}\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Calculate $2$ to the power of $2$ and get $4$.

$$8100\sqrt{216\times 4\times 3^{2}\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Multiply $216$ and $4$ to get $864$.

$$8100\sqrt{864\times 3^{2}\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

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

$$8100\sqrt{864\times 9\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Multiply $864$ and $9$ to get $7776$.

$$8100\sqrt{7776\times 4^{2}\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Calculate $4$ to the power of $2$ and get $16$.

$$8100\sqrt{7776\times 16\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Multiply $7776$ and $16$ to get $124416$.

$$8100\sqrt{124416\times 5^{2}\times 7^{2}\times 8^{2}\times 9^{2}}$$

Calculate $5$ to the power of $2$ and get $25$.

$$8100\sqrt{124416\times 25\times 7^{2}\times 8^{2}\times 9^{2}}$$

Multiply $124416$ and $25$ to get $3110400$.

$$8100\sqrt{3110400\times 7^{2}\times 8^{2}\times 9^{2}}$$

Calculate $7$ to the power of $2$ and get $49$.

$$8100\sqrt{3110400\times 49\times 8^{2}\times 9^{2}}$$

Multiply $3110400$ and $49$ to get $152409600$.

$$8100\sqrt{152409600\times 8^{2}\times 9^{2}}$$

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

$$8100\sqrt{152409600\times 64\times 9^{2}}$$

Multiply $152409600$ and $64$ to get $9754214400$.

$$8100\sqrt{9754214400\times 9^{2}}$$

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

$$8100\sqrt{9754214400\times 81}$$

Multiply $9754214400$ and $81$ to get $790091366400$.

$$8100\sqrt{790091366400}$$

Factor $790091366400=362880^{2}\times 6$. Rewrite the square root of the product $\sqrt{362880^{2}\times 6}$ as the product of square roots $\sqrt{362880^{2}}\sqrt{6}$. Take the square root of $362880^{2}$.

$$8100\times 362880\sqrt{6}$$

Multiply $8100$ and $362880$ to get $2939328000$.

$$2939328000\sqrt{6}$$