simplify 5sqrt(28)+sqrt(63) — step-by-step solution

Let's reduce:

5 \times \sqrt{28} + \sqrt{63}

ⓘ We look for the largest square dividing

28

4

2^{2}

, and take it out of the root:

\sqrt{28}

\sqrt{4 \times 7}

\sqrt{4} \times \sqrt{7}

2 \times \sqrt{7}

■We look for the largest square dividing

63

9

3^{2}

, and take it out of the root:

\sqrt{63}

\sqrt{9 \times 7}

\sqrt{9} \times \sqrt{7}

3 \times \sqrt{7}

5 \times 2 \times \sqrt{7} + 3 \times \sqrt{7}

ⓘ Multiplications are done before additions and subtractions:

5 \times 2

10

10 \times \sqrt{7} + 3 \times \sqrt{7}

ⓘ Like terms are grouped by adding their coefficients:

10 \times \sqrt{7} + 3 \times \sqrt{7}

13 \times \sqrt{7}

▶Simplified form:

13 \times \sqrt{7}

The numeric value of:

13 \times \sqrt{7}

equals:

13 \times \approx 2.6458

▷

\approx 34.3948