Perfect Square In our previous video, we learned about square and square roots. We’ve already known that
the square roots operation is the inverse of the squaring operation. For example, when you square 5, you get 25, and its square root is 5. Similarly, 7 squared is 49, therefore the square root of 49 is 7. These special numbers, like 25 and 49, are called perfect squares. Just like in life,
some are perfect and some are not! A perfect square can be expressed as the product of two integers of
equal value. For instance,
9 is a perfect square, because it is the result of
3 multiplied by 3. Now, to determine whether a number, namely 134 is a perfect square, check if it can be expressed as
the product of two equal integers. In this case, 134 is not a perfect square because
it falls between two perfect squares: 121 (from 11 squared) and 144 (from 12 squared), and therefore not an integer. The square root is a decimal number
(11.576) What about the numbers 27, 73, 188, 362, 527, and 903? A
re any of them perfect squares? Answer it without a calculator
in under 5 seconds! Remember, in the world of perfect squares, the unit digit (the last digit)
follows specific patterns: 0, 1, 4, 5, 6 or 9. However,
it does not work in the opposite way, as seen with 79,
which isn’t a perfect square despite ending in 9. So, always keep in mind that if the unit digit is 2, 3, 7 or 8,
the number is definitely not a perfect square. This rule applies even to larger numbers. For instance, consider the n
umber
1,679,743 Since it ends with 3,
it is not a perfect square, which means no two integers of equal value will ever give the product as
1,679,743. All perfect squares have
two sets of square roots. Consider a perfect square 81. The product 81 can be obtained
by multiplying two sets of integers. 9 x 9 and (-9) x (-9) A positive value of 9 multiplied by itself will yield 81,
just like a negative value of 9 will. Similarly, we can say that
the square roots of 49 are -7 and +7. Now, let’s put you
r knowledge to the test! Can you quickly determine if
the following numbers are perfect squares? 256, 625, 729, 972 Rely on the patterns we discussed earlier! Leave your answers in the comments below! If you enjoyed our perfect squares lesson,
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