What is the answer to this problem with explanation?

Question

What is the answer to this problem with explanation?

$(3 \sqrt{10} + 5) (4 \sqrt{6} - 2)$ $(3sqrt10+5)(4sqrt6-2)$

2 Answers

Impact of this question

1338 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-18T07:55:59

$24 \sqrt{15} - 6 \sqrt{10} + 20 \sqrt{6} - 10$ $24sqrt15-6sqrt10+20sqrt6-10$

Explanation:

$using the law of radicals$ $"using the "color(blue)"law of radicals"$

$∙ x \sqrt{a} \times \sqrt{b} \Leftrightarrow \sqrt{a b}$ $•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)$

$expand the factors using FOIL$ $"expand the factors using FOIL"$

$= (3 \sqrt{10} \times 4 \sqrt{6}) + (- 2 \times 3 \sqrt{10}) + (5 \times 4 \sqrt{6})$ $=(3sqrt10xx4sqrt6)+(-2xx3sqrt10)+(5xx4sqrt6)$
$= + (5 \times - 2)$ $color(white)(=)+(5xx-2)$

$= 12 \sqrt{60} - 6 \sqrt{10} + 20 \sqrt{6} - 10$ $=12sqrt60-6sqrt10+20sqrt6-10$

$\sqrt{10} and \sqrt{6} are in simplest form$ $sqrt10" and "sqrt6" are in simplest form"$

$\sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \times \sqrt{15} = 2 \sqrt{15}$ $sqrt60=sqrt(4xx15)=sqrt4xxsqrt15=2sqrt15$

$\sqrt{15} is in simplest form$ $sqrt15" is in simplest form"$

$= (12 \times 2 \sqrt{15}) - 6 \sqrt{10} + 20 \sqrt{6} - 10$ $=(12xx2sqrt15)-6sqrt10+20sqrt6-10$

$= 24 \sqrt{15} - 6 \sqrt{10} + 20 \sqrt{6} - 10$ $=24sqrt15-6sqrt10+20sqrt6-10$

Answer 2 · 2018-06-18T07:56:07

$48 \sqrt{15} - 6 \sqrt{10} + 20 \sqrt{6} - 10$ $48sqrt15-6sqrt10+20sqrt6-10$
See below

Explanation:

We have to operate in this expresion usin distributive law for real numbers. This property stablish

$(a + d) (b + c) = a b + a c + d b + d c$ $(a+d)(b+c)=ab+ac+db+dc$

$(3 \sqrt{10} + 5) (4 \sqrt{6} - 2) = 3 \sqrt{10} \cdot 4 \sqrt{6} - 3 \sqrt{10} \cdot 2 + 5 \cdot 4 \sqrt{6} - 5 \cdot 2 = 12 \sqrt{10} \sqrt{6} - 6 \sqrt{10} + 20 \sqrt{6} - 10$ $(3sqrt10+5)(4sqrt6-2)=3sqrt10·4sqrt6-3sqrt10·2+5·4sqrt6-5·2=12sqrt10sqrt6-6sqrt10+20sqrt6-10$

But $\sqrt{10} \sqrt{6} = \sqrt{60} = \sqrt{5 \cdot 2^{2} \cdot 3} = 2 \sqrt{15}$ $sqrt10sqrt6=sqrt60=sqrt(5·2^2·3)=2sqrt15$

Then

$12 \sqrt{10} \sqrt{6} - 6 \sqrt{10} + 20 \sqrt{6} - 10 = 24 \sqrt{15} - 6 \sqrt{10} + 20 \sqrt{6} - 10$ $12sqrt10sqrt6-6sqrt10+20sqrt6-10=24sqrt15-6sqrt10+20sqrt6-10$

Science

Math

Humanities

... and beyond

What is the answer to this problem with explanation?

$(3 \sqrt{10} + 5) (4 \sqrt{6} - 2)$ $(3sqrt10+5)(4sqrt6-2)$

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the answer to this problem with explanation?

(3√10+5)(4√6−2)(3sqrt10+5)(4sqrt6-2)

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

$(3 \sqrt{10} + 5) (4 \sqrt{6} - 2)$ $(3sqrt10+5)(4sqrt6-2)$