Question

2. Jaclyn estimates the square root of 50 in the following way:

/50 = 2/ 25 = 2 □5=10
(A) Explain why her reasoning is incorrect.
(B) Estimate the square root of 50 to the nearest tenth without using your calculators. Show your work.
Answer:​

Answer 1

B is 7.1!

Explanation:

Answer 2

(B) 7.1 is the estimated square root of 50

Explanation:

A. √50 = √2 √25

= 5√2.

Jaclyn did not take the square root of 2.

B. We estimate the square root of 2.

Trial and improvement:

It must lie between 1 and 2 so we try 1.5:

1.5 * 1.5 = 2.25

Its < 1.5 so try 1.4

1.4 * 1.4 = 1.96.

So it is a little above 1.4.

Try 1.45:

1.45 * 1.45

1.45

* 1.45

-------

725

5800

14500

2.1025

= 2.1025.

- this is above 2 so the answer is between 1.40 and 1.45 but closer to 1.4.

A good estimate is 1.42

So the square root of 50 is about 5*1.42 = 7.1