Evaluate seventh root of (4.5*10^4)+235

$\sqrt[7]{(4.5 \cdot 10^{4}) + 235}$

Step 1

Convert $235$ to scientific notation.

$\sqrt[7]{4.5 \cdot 10^{4} + 2.35 \cdot 10^{2}}$

Step 2

Move the decimal point in $2.35$ to the left by $2$ places and increase the power of $10^{2}$ by $2$ .

$\sqrt[7]{4.5 \cdot 10^{4} + 0.0235 \cdot 10^{4}}$

Step 3

Factor $10^{4}$ out of $4.5 \cdot 10^{4} + 0.0235 \cdot 10^{4}$ .

$\sqrt[7]{(4.5 + 0.0235) \cdot 10^{4}}$

Step 4

Simplify the expression.

Add $4.5$ and $0.0235$ .

$\sqrt[7]{4.5235 \cdot 10^{4}}$

Rewrite $4.5235 \cdot 10^{4}$ as $0.0045235 \cdot 10^{7}$ .

$\sqrt[7]{0.0045235 \cdot 10^{7}}$

Step 5

Rewrite $\sqrt[7]{0.0045235 \cdot 10^{7}}$ as $\sqrt[7]{0.0045235} \cdot \sqrt[7]{10^{7}}$ .

$\sqrt[7]{0.0045235} \cdot \sqrt[7]{10^{7}}$

Step 6

Evaluate the root.

$0.46245321 \cdot \sqrt[7]{10^{7}}$

Step 7

Pull terms out from under the radical, assuming real numbers.

$0.46245321 \cdot 10$

Step 8

Raise $10$ to the power of $1$ .

$0.46245321 \cdot 10^{1}$

Step 9

Move the decimal point in $0.46245321$ to the right by $1$ place and decrease the power of $10^{1}$ by $1$ .

$4.6245321 \cdot 10^{0}$

Step 10

Convert $4.6245321 \cdot 10^{0}$ from scientific notation.

$4.6245321$