Question

1)Give two numbers whose square roots add up to 5.

2)Give two numbers whose cube roots add up to 9.


Pls Help Me.

Answer 1

1) 25, 0 or 16, 1 or 9, 4

2) 0, 729 or 1, 512 or 8, 343 or 27, 216 or 64, 125

Explanation:

1) Let x and y are the numbers,

∵ √x + √y = 5

⇒ √x ≤ 5 and √y ≤ 5

⇒ x ≤ 25 and y ≤ 25

Thus, the possible values of x or y,

{25, 16, 9, 4, 1, 0}

If √x + √y = 5 then the possible pairs,

{(25, 0), (16, 1), (9, 4), }

Hence, the possible pairs of numbers whose square roots add up to 5 are,

25, 0 or 16, 1 or 9, 4

2) Let u and v are the numbers

∵ ∛u + ∛v = 9

∛u ≤ 9, ∛v ≤ 9

⇒ u ≤ 729, v ≤ 729

So, the possible values of u or v,

{ 0, 1, 8, 27, 64, 125, 216, 343, 512, 729 }

Hence, the possible pairs whose cube roots add up to 9 are,

0, 729 or 1, 512 or 8, 343 or 27, 216 or 64, 125

Answer 2

For example,

1) 9 and 4

2) 9 and 36

Explanation:

1) Give two numbers whose square roots add up to 5.

Consider such numbers:

`x_1=9\\ \\x_2=4`

Then

`√(x_1)=√(9)=3\\ \\√(x_2)=√(4)=2`

Therefore,

`√(x_1)+√(x_2)=3+2=5`

2) Give two numbers whose square roots add up to 9.

Consider such numbers:

`x_1=9\\ \\x_2=36`

Then

`√(x_1)=√(9)=3\\ \\√(x_2)=√(36)=6`

Therefore,

`√(x_1)+√(x_2)=3+6=9`