Question

squares and square roots
to find the square of a number, you multiply the number by itself
for example: the square of the number 5 equals 5·5 = 25.
the square of 7 is 7·7 = 49. another way to express the square of a number is
by using the superscript 2.
the square of 7 is 7² = 7·7 = 49
the square of 9 is 9² = 9·9 = 81
calculator method: using the key
to find the 9² using a calculator.

1. enter 9 → display 9
2. press → display 81 (81 is the answer)

exercises: complete the following finding the squares of each number.
(1) 5² = 5·5 = 25 (2) 1² = · =
(3) 2² = · = (4) 10² = · =
(5) 6² = · = (6) 11² = · =
(7) 3² = · = (8) 12² = · =
(9) 15² = · = (10) 7² = · =
the principle square root of a number is defined as follows:
if a·a = a², then the square root of a² = a. √ means the square root of
in other words, if 2·2 = 4 then √4 = 2
this is read the square root of 4 equals 2.
√ is called a radical.
examples:
find the principle square root of the following:
(1) √81
solution: because 81 = 9·9 = 9 (9·9 = 81)
this is read the square root of 81 equals 9. therefore √81 = 9

Explanation:

Step1: Calculate \(1^{2}\)

According to the rule \(a^{2}=a\times a\), for \(a = 1\), we have \(1^{2}=1\times1\).

$$1\times1 = 1$$

Step2: Calculate \(2^{2}\)

Using the formula \(a^{2}=a\times a\) with \(a = 2\), we get \(2^{2}=2\times2\).

$$2\times2=4$$

Step3: Calculate \(10^{2}\)

Applying the formula \(a^{2}=a\times a\) where \(a = 10\), we have \(10^{2}=10\times10\).

$$10\times10 = 100$$

Step4: Calculate \(6^{2}\)

By the formula \(a^{2}=a\times a\) for \(a = 6\), \(6^{2}=6\times6\).

$$6\times6=36$$

Step5: Calculate \(11^{2}\)

Using \(a^{2}=a\times a\) with \(a = 11\), we get \(11^{2}=11\times11\).

$$11\times11 = 121$$

Step6: Calculate \(3^{2}\)

Applying the formula \(a^{2}=a\times a\) where \(a = 3\), \(3^{2}=3\times3\).

$$3\times3=9$$

Step7: Calculate \(12^{2}\)

By the formula \(a^{2}=a\times a\) for \(a = 12\), \(12^{2}=12\times12\).

$$12\times12 = 144$$

Step8: Calculate \(15^{2}\)

Using \(a^{2}=a\times a\) with \(a = 15\), we get \(15^{2}=15\times15\).

$$15\times15=225$$

Step9: Calculate \(7^{2}\)

Applying the formula \(a^{2}=a\times a\) where \(a = 7\), \(7^{2}=7\times7\).

$$7\times7 = 49$$

Answer:

(2) \(1^{2}=1\cdot1 = 1\)
(3) \(2^{2}=2\cdot2=4\)
(4) \(10^{2}=10\cdot10 = 100\)
(5) \(6^{2}=6\cdot6=36\)
(6) \(11^{2}=11\cdot11 = 121\)
(7) \(3^{2}=3\cdot3=9\)
(8) \(12^{2}=12\cdot12 = 144\)
(9) \(15^{2}=15\cdot15=225\)
(10) \(7^{2}=7\cdot7 = 49\)