b Identify perfect squares above and below the given radicands.
A
a sqrt(68)≈ 8.2, see solution.
B
b sqrt(5)≈ 2.2
sqrt(85)≈ 9.2
sqrt(50)≈ 7.1
sqrt(22)≈ 4.7
Practice makes perfect
a We cannot calculate sqrt(68) because the radicand is not a perfect square. However, we can estimate it by using other perfect squares that are close to it, one below and one above 68. Let's list some perfect squares.
x
x^2
=
2
2^2
4
3
3^2
9
4
4^2
16
5
5^2
25
6
6^2
36
7
7^2
49
8
8^2
64
9
9^2
81
10
10^2
100
From the table, we see that 68 is between 64 and 81, which are perfect squares of 8 and 9. Therefore, sqrt(68) must be between 8 and 9
sqrt(64)
b We can reuse the table from Part A to approximate the given radicals.
sqrt(5), sqrt(85), sqrt(50), sqrt(22)
Like in Part A, this only tells us between which perfect squares the radicals will fall and not their exact value. We can highlight the perfect squares between which the values will fall.
x
x^2
=
2
2^2
4
3
3^2
9
4
4^2
16
5
5^2
25
6
6^2
36
7
7^2
49
8
8^2
64
9
9^2
81
10
10^2
100
Using the same logic from Part A, we can write intervals for each square root.
