Solve (1)-sqrt{(-2)^2}-sqrt{125/144}+2/5*sqrt[3]{-125}=-51/12*(2)(7/3)

$$( 1 ) - \sqrt { ( - 2 ) ^ { 2 } } - \sqrt { 1 \frac { 25 } { 144 } } + \frac { 2 } { 5 } \times \sqrt[ 3 ] { - 125 } = - 5 \frac { 1 } { 12 } \cdot ( 2 ) ( \frac { 7 } { 3 } )$$

Verify

Solution Steps

Multiply both sides of the equation by 60, the least common multiple of 5,12,3.

$$60-60\sqrt{\left(-2\right)^{2}}-60\sqrt{\frac{144+25}{144}}+24\sqrt[3]{-125}=60\left(-\frac{5\times 12+1}{12}\right)\times 2\times \frac{7}{3}$$

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

$$60-60\sqrt{4}-60\sqrt{\frac{144+25}{144}}+24\sqrt[3]{-125}=60\left(-\frac{5\times 12+1}{12}\right)\times 2\times \frac{7}{3}$$

Calculate the square root of 4 and get 2.

$$60-60\times 2-60\sqrt{\frac{144+25}{144}}+24\sqrt[3]{-125}=60\left(-\frac{5\times 12+1}{12}\right)\times 2\times \frac{7}{3}$$

Multiply -60 and 2 to get -120.

$$60-120-60\sqrt{\frac{144+25}{144}}+24\sqrt[3]{-125}=60\left(-\frac{5\times 12+1}{12}\right)\times 2\times \frac{7}{3}$$

Subtract 120 from 60 to get -60.

$$-60-60\sqrt{\frac{144+25}{144}}+24\sqrt[3]{-125}=60\left(-\frac{5\times 12+1}{12}\right)\times 2\times \frac{7}{3}$$

Add 144 and 25 to get 169.

$$-60-60\sqrt{\frac{169}{144}}+24\sqrt[3]{-125}=60\left(-\frac{5\times 12+1}{12}\right)\times 2\times \frac{7}{3}$$

Rewrite the square root of the division \frac{169}{144} as the division of square roots \frac{\sqrt{169}}{\sqrt{144}}. Take the square root of both numerator and denominator.

$$-60-60\times \frac{13}{12}+24\sqrt[3]{-125}=60\left(-\frac{5\times 12+1}{12}\right)\times 2\times \frac{7}{3}$$

Multiply -60 and \frac{13}{12} to get -65.

$$-60-65+24\sqrt[3]{-125}=60\left(-\frac{5\times 12+1}{12}\right)\times 2\times \frac{7}{3}$$

Subtract 65 from -60 to get -125.

$$-125+24\sqrt[3]{-125}=60\left(-\frac{5\times 12+1}{12}\right)\times 2\times \frac{7}{3}$$

Calculate \sqrt[3]{-125} and get -5.

$$-125+24\left(-5\right)=60\left(-\frac{5\times 12+1}{12}\right)\times 2\times \frac{7}{3}$$

Multiply 24 and -5 to get -120.

$$-125-120=60\left(-\frac{5\times 12+1}{12}\right)\times 2\times \frac{7}{3}$$

Subtract 120 from -125 to get -245.

$$-245=60\left(-\frac{5\times 12+1}{12}\right)\times 2\times \frac{7}{3}$$

Multiply 5 and 12 to get 60.

$$-245=60\left(-\frac{60+1}{12}\right)\times 2\times \frac{7}{3}$$

Add 60 and 1 to get 61.

$$-245=60\left(-\frac{61}{12}\right)\times 2\times \frac{7}{3}$$

Multiply 60 and -\frac{61}{12} to get -305.

$$-245=-305\times 2\times \frac{7}{3}$$

Multiply -305 and 2 to get -610.

$$-245=-610\times \frac{7}{3}$$

Multiply -610 and \frac{7}{3} to get -\frac{4270}{3}.

$$-245=-\frac{4270}{3}$$

Convert -245 to fraction -\frac{735}{3}.

$$-\frac{735}{3}=-\frac{4270}{3}$$

Compare -\frac{735}{3} and -\frac{4270}{3}.

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