Solve sqrt[4] 144- sqrt[4] 1250 - sqrt[4] 32+ sqrt[4] 52 | 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

$$\sqrt[4]{144-\sqrt[4]{1250}-\sqrt[4]{32+\sqrt[4]{52}}$$

Evaluate

$\frac{11\sqrt{5}}{227892523230000}+6\sqrt{409}\approx 121.342490497$

Solution Steps

Subtract $8$ from $1644$ to get $1636$.

$$3\sqrt{1636}+\frac{81780^{-3}\times 132}{5}\sqrt{5}$$

Factor $1636=2^{2}\times 409$. Rewrite the square root of the product $\sqrt{2^{2}\times 409}$ as the product of square roots $\sqrt{2^{2}}\sqrt{409}$. Take the square root of $2^{2}$.

$$3\times 2\sqrt{409}+\frac{81780^{-3}\times 132}{5}\sqrt{5}$$

Multiply $3$ and $2$ to get $6$.

$$6\sqrt{409}+\frac{81780^{-3}\times 132}{5}\sqrt{5}$$

Calculate $81780$ to the power of $-3$ and get $\frac{1}{546942055752000}$.

$$6\sqrt{409}+\frac{\frac{1}{546942055752000}\times 132}{5}\sqrt{5}$$

Multiply $\frac{1}{546942055752000}$ and $132$ to get $\frac{11}{45578504646000}$.

$$6\sqrt{409}+\frac{\frac{11}{45578504646000}}{5}\sqrt{5}$$

Express $\frac{\frac{11}{45578504646000}}{5}$ as a single fraction.

$$6\sqrt{409}+\frac{11}{45578504646000\times 5}\sqrt{5}$$

Multiply $45578504646000$ and $5$ to get $227892523230000$.

$$6\sqrt{409}+\frac{11}{227892523230000}\sqrt{5}$$

Factor

$\frac{11 \sqrt{5} + 1367355139380000 \sqrt{409}}{227892523230000} = 121\frac{78051023530000}{227892523230000} = 121.3424904969402$