Solve sqrt[5]{-32*243}+sqrt{100*4*25}-0,5sqrt[3]{27*125}+sqrt{25*169}

$$\sqrt[ 5 ] { - 32 \cdot 243 } + \sqrt { 100 \cdot 4 \cdot 25 } - 0,5 \sqrt[ 3 ] { 27 \cdot 125 } + \sqrt { 25 \cdot 169 }$$

Evaluate

$$151,5$$

Solution Steps

Multiply -32 and 243 to get -7776.

$$\sqrt[5]{-7776}+\sqrt{100\times 4\times 25}-0,5\sqrt[3]{27\times 125}+\sqrt{25\times 169}$$

Calculate \sqrt[5]{-7776} and get -6.

$$-6+\sqrt{100\times 4\times 25}-0,5\sqrt[3]{27\times 125}+\sqrt{25\times 169}$$

Multiply 100 and 4 to get 400.

$$-6+\sqrt{400\times 25}-0,5\sqrt[3]{27\times 125}+\sqrt{25\times 169}$$

Multiply 400 and 25 to get 10000.

$$-6+\sqrt{10000}-0,5\sqrt[3]{27\times 125}+\sqrt{25\times 169}$$

Calculate the square root of 10000 and get 100.

$$-6+100-0,5\sqrt[3]{27\times 125}+\sqrt{25\times 169}$$

Add -6 and 100 to get 94.

$$94-0,5\sqrt[3]{27\times 125}+\sqrt{25\times 169}$$

Multiply 27 and 125 to get 3375.

$$94-0,5\sqrt[3]{3375}+\sqrt{25\times 169}$$

Calculate \sqrt[3]{3375} and get 15.

$$94-0,5\times 15+\sqrt{25\times 169}$$

Multiply 0,5 and 15 to get 7,5.

$$94-7,5+\sqrt{25\times 169}$$

Subtract 7,5 from 94 to get 86,5.

$$86,5+\sqrt{25\times 169}$$

Multiply 25 and 169 to get 4225.

$$86,5+\sqrt{4225}$$

Calculate the square root of 4225 and get 65.

$$86,5+65$$

Add 86,5 and 65 to get 151,5.

$$151,5$$

Factor

$$\frac{3 \cdot 101}{2} = 151\frac{1}{2} = 151.5$$