Question

1- Can we get an irrational number by multiplying two rational numbers?

2- Can we get a rational number by multiplying two irrational numbers?

3- Solve the following:

(a) √10 × √5 (b) √3 × √6

(c) √6 (√3 + 2) (d) √15 » √5

(e) √7 × √21 (f) 18√3 » 6√3

(g) 27.8 × 15 (h) 1.06 » 2​

Answer 1

Step-by-step explanation:

1. It will be always rational.

Ex-2*3 , 3*3, etc.

2. Yes, we can get.

Ex - √2 * √2 = 2

3.a, √50 or 5√2

b. √18 or 3√2

c. 3√2 + 2√6

d. 5√3

e. 7√3

f. 324 (18 * 6 * 3)

g. 417

h. 2.12

Hope this helps...

Answer 2

Step-by-step explanation:

1- Can we get an irrational number by multiplying two rational numbers?

Ans: No

Justification: Two rational number always produced a rational number after multiplication.

2- Can we get a rational number by multiplying two irrational numbers?

Ans: Yes

Solution: Taking √3+√2

and √3 - √2

two different irrational numbers

Now multiply these two

$( \sqrt{3} + \sqrt{2} )( \sqrt{3} - \sqrt{2} ) \\ \\ = {( \sqrt{3} )}^{2} - ( { \sqrt{2} )}^{2} \\ \\ = 3 - 2 \\ \\ = 1 \: \: (a \: rational \: number)$

3- Solve the following:

(a) √10 × √5

Ans: √50 = 5√2 (an irrational number)

(b) √3 × √6

Ans: √18 = 3√2 (an irrational number)

(c) √6 (√3 + 2)

Ans: √6 ×√3+2√6

=>√18+2√6

=>3√2+2√6

(an irrational number)

(d) √15 ÷ √5

Ans: √(5×3)÷√5

=> √5×√3÷√5

=>√3

(an irrational number)

(e) √7 × √21

Ans: √(7×21)

=>√(7×7×3)

=>7√3

(an irrational number)

(f) 18√3 ÷ 6√3

Ans: 6×3√3÷6√3

=3

(a rational number)

(g) 27.8 × 15

Ans: 417

(h) 1.06 ^ 2

Ans:

(106/100)^2

=(106×106)÷10000

=11236/10000

=1.1236

Hope it helps you.