**Estimate square roots :**

As soon as we saw a number, we can tell that the square root of the given number lies between these two numbers.

For example square root of the number 40 lies between 6 and 7.

Because square root of 36 is 6 and square root of 49 is 7. The given number lies between 36 and 49. So that we can say that the square root of the given number is between 6 and 7.

From the above table we come to know that

- (i) If a perfect square has ‘n’ digits where n is even, its square root has n/2 digits.
- (ii) If a perfect square has ‘n’ digits where n is odd, its square root has (n + 1)/2 digits.

**Example 1 :**

Estimate the value of the following to the nearest whole number.

√80

**Solution :**

√64 < √80 < √81

8 < √80 < 9

Since the given number lies between 64 and 81, the approximate square root of the given number is 8.

Hence the approximate value of √80 is 8.

**Example 2 :**

Estimate the value of the following to the nearest whole number.

√1000

**Solution :**

The given number is greater than 900. If we multiply 32 x 32 we will get 1024 which is greater than 1000. So we have to try the number less than 32 but greater than 30.

31 x 31 = 961 < 1000

Hence the approximate square root of 100 is 31.

**Example 3 :**

Estimate the value of the following to the nearest whole number.

√172

**Solution :**

The given number is greater than 169 and lesser than 196. So the square root of the given number lies between 16 and 17.

Hence the approximate square root of 172 is 16.

**Example 4 :**

Estimate the value of the following to the nearest whole number.

√5928

**Solution :**

Number of digits in the given number = 4

So, square root of 5928 will have 2 digits.

70 x 70 = 4900

75 x 75 = 5625

77 x 77 = 5929

Hence the approximate square root of 5928 is 76.

After having gone through the stuff given above, we hope that the students would have understood "Estimate square roots".

Apart from the stuff given above, if you want to know more about "Estimate square roots" Please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**