Simplify the expression completely. -sqrt49+2root(3)(-729)+sqrt(-9)+5sqrt(-49) Answer:

Find Square Root: First, we simplify each term in the expression separately. Starting with the first term, -sqrt(49), we find the square root of 49 and then apply the negative sign. sqrt(49) = 7 So, -sqrt(49) = -7Calculate Cube Root: Next, we simplify the second term, 2root(3)(-729). We need to find the cube root of -729 and then multiply it by 2. The cube root of -729 is -9 because (-9)^3 = -729. So, 2root(3)(-729) = 2 * (-9) = -18Evaluate Imaginary Square Root: Now, we simplify the third term, sqrt(-9). Since the square root of a negative number is not a real number, we express it in terms of i, where i is the imaginary unit with the property that i^2 = -1. sqrt(-9) = sqrt(9) * sqrt(-1) = 3iSimplify with Imaginary Unit: Finally, we simplify the fourth term, 5sqrt(-49). Similar to the third term, we express the square root of a negative number in terms of i. sqrt(-49) = sqrt(49) * sqrt(-1) = 7i So, 5sqrt(-49) = 5 * 7i = 35iCombine Simplified Terms: Now we combine all the simplified terms to find the final answer. -7 - 18 + 3i + 35i = -25 + 38i

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Simplify the expression completely.

-sqrt49+2root(3)(-729)+sqrt(-9)+5sqrt(-49)
Answer:

Simplify the expression completely. $\newline$ $-\sqrt{49}+2 \sqrt[3]{-729}+\sqrt{-9}+5 \sqrt{-49}$ $\newline$ Answer:

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Algebra 2

Sum of finite series starts from 1

Full solution

Q. Simplify the expression completely.

\newline

-\sqrt{49}+2 \sqrt[3]{-729}+\sqrt{-9}+5 \sqrt{-49}

\newline

Answer:

Find Square Root: First, we simplify each term in the expression separately. Starting with the first term, $-\sqrt{49}$ , we find the square root of $49$ and then apply the negative sign. $\newline$ $\sqrt{49} = 7$ $\newline$ So, $-\sqrt{49} = -7$
Calculate Cube Root: Next, we simplify the second term, $2\sqrt[3]{-729}$ . We need to find the cube root of $-729$ and then multiply it by $2$ . $\newline$ The cube root of $-729$ is $-9$ because $(-9)^3 = -729$ . $\newline$ So, $2\sqrt[3]{-729} = 2 \times (-9) = -18$
Evaluate Imaginary Square Root: Now, we simplify the third term, $\sqrt{-9}$ . Since the square root of a negative number is not a real number, we express it in terms of $i$ , where $i$ is the imaginary unit with the property that $i^2 = -1$ . $\newline$ $\sqrt{-9} = \sqrt{9} \cdot \sqrt{-1} = 3i$
Simplify with Imaginary Unit: Finally, we simplify the fourth term, $5\sqrt{-49}$ . Similar to the third term, we express the square root of a negative number in terms of $i$ . $\newline$ $\sqrt{-49} = \sqrt{49} \times \sqrt{-1} = 7i$ $\newline$ So, $5\sqrt{-49} = 5 \times 7i = 35i$
Combine Simplified Terms: Now we combine all the simplified terms to find the final answer. $\newline$ $-7 - 18 + 3i + 35i = -25 + 38i$