Solve sqrt[3]{27}-4sqrt{64}+3sqrt[4]{625}+5sqrt{25}-9sqrt{2}

$$\sqrt[ 3 ] { 27 } - 4 \sqrt { 64 } + 3 \sqrt[ 4 ] { 625 } + 5 \sqrt { 25 } - 9 \sqrt { 2 }$$

Evaluate

$$11-9\sqrt{2}\approx -1.727922061$$

Solution Steps

Calculate \sqrt[3]{27} and get 3.

$$3-4\sqrt{64}+3\sqrt[4]{625}+5\sqrt{25}-9\sqrt{2}$$

Calculate the square root of 64 and get 8.

$$3-4\times 8+3\sqrt[4]{625}+5\sqrt{25}-9\sqrt{2}$$

Multiply -4 and 8 to get -32.

$$3-32+3\sqrt[4]{625}+5\sqrt{25}-9\sqrt{2}$$

Subtract 32 from 3 to get -29.

$$-29+3\sqrt[4]{625}+5\sqrt{25}-9\sqrt{2}$$

Calculate \sqrt[4]{625} and get 5.

$$-29+3\times 5+5\sqrt{25}-9\sqrt{2}$$

Multiply 3 and 5 to get 15.

$$-29+15+5\sqrt{25}-9\sqrt{2}$$

Add -29 and 15 to get -14.

$$-14+5\sqrt{25}-9\sqrt{2}$$

Calculate the square root of 25 and get 5.

$$-14+5\times 5-9\sqrt{2}$$

Multiply 5 and 5 to get 25.

$$-14+25-9\sqrt{2}$$

Add -14 and 25 to get 11.

$$11-9\sqrt{2}$$