Solve tsqrt{(-5)^2*3^7}

$$t \sqrt { ( - 5 ) ^ { 2 } \times 3 ^ { 7 } }$$

Evaluate

$$135\sqrt{3}t$$

Solution Steps

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

$$t\sqrt{25\times 3^{7}}$$

Calculate 3 to the power of 7 and get 2187.

$$t\sqrt{25\times 2187}$$

Multiply 25 and 2187 to get 54675.

$$t\sqrt{54675}$$

Factor 54675=135^{2}\times 3. Rewrite the square root of the product \sqrt{135^{2}\times 3} as the product of square roots \sqrt{135^{2}}\sqrt{3}. Take the square root of 135^{2}.

$$t\times 135\sqrt{3}$$

Differentiate w.r.t. t

$$135 \sqrt{3} = 233.826859022$$