simplify 4sqrt(160)+2sqrt(40) — step-by-step solution

Let's reduce:

4 \times \sqrt{160} + 2 \times \sqrt{40}

ⓘ We look for the largest square dividing

160

16

4^{2}

, and take it out of the root:

\sqrt{160}

\sqrt{16 \times 10}

\sqrt{16} \times \sqrt{10}

4 \times \sqrt{10}

■We look for the largest square dividing

40

4

2^{2}

, and take it out of the root:

\sqrt{40}

\sqrt{4 \times 10}

\sqrt{4} \times \sqrt{10}

2 \times \sqrt{10}

4 \times 4 \times \sqrt{10} + 2 \times 2 \times \sqrt{10}

ⓘ Multiplications are done before additions and subtractions:

4 \times 4

16

2 \times 2

4

16 \times \sqrt{10} + 4 \times \sqrt{10}

ⓘ Like terms are grouped by adding their coefficients:

16 \times \sqrt{10} + 4 \times \sqrt{10}

20 \times \sqrt{10}

▶Simplified form:

20 \times \sqrt{10}

The numeric value of:

20 \times \sqrt{10}

is:

20 \times \approx 3.1623

▷

\approx 63.2456