Square Roots and Cube Roots
Approximating square roots
Since 62 = 36 and 72 = 49, then is between and .
Therefore, is a value between 6 and 7. Since 42 is about halfway between 36 and 49, you can expect that will be close to halfway between 6 and 7, or about 6.5. To check this estimation, 6.5 × 6.5 = 42.25, or about 42.
Square roots of nonperfect squares can be approximated, looked up in tables, or found by using a calculator. You may want to keep these two in mind:
Simplifying square roots
, the largest perfect square is easy to see, and Method 1 probably is a faster method.
, it is not so obvious that the largest perfect square is 144, so Method 2 is probably the faster method.Many square roots cannot be simplified because they are already in simplest form, such as , , and .
1. The cube root of .000216 is:
2.The least perfect square, which is divisible by each of 21, 36 and 66 is:
3.A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:
4. If a = 0.1039, then the value of 4a2 - 4a + 1 + 3a is:
5.How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 8 ?
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