Question

Of course, you don't know what the dropdowns are, so, I'll tell you.

4 < 5 < 9, so √5 is between (3, 4, the square root of 3, the square root of 4) and (6, 9, the square root of 6, the square root of 9).

This means that √5 is between (4 and 9, 2 and 3, 4 and 6, square root of 2 and square root of 3).

So, √65 is between (6 x 2, 6 x 3, 6 x 4) and (6 x 3, 6 x 6, 6 x 9).

Thank you and please help me!

Answer 1

Part A

4 < 5 < 9 is given to us. Apply the square root to each term to end up with this inequality: sqrt(4) < sqrt(5) < sqrt(9)

So sqrt(5) is between sqrt(4) and sqrt(9)

-------------------

Part B

Simplify those two mentioned square roots

sqrt(4) = sqrt(2^2) = 2

sqrt(9) = sqrt(3^2) = 3

Therefore, sqrt(5) is also between 2 and 3

We can see this through using a calculator: sqrt(5) = 2.23607 approximately

-----------------

Part C

We can now say:

2 < sqrt(5) < 3

Multiply all three sides by 6

6*2 < 6*sqrt(5) < 6*3

So the expression 6*sqrt(5) is between 6 x 2 and 6 x 3

Sure enough, a calculator confirms this

6*sqrt(5) = 13.416408

since 6*2 = 12 and 6*3 = 18. We see that 13.416 is between 12 and 18.