**Square and Square Root Tricks Math Tricks Problems and Solutions**

**Square and Square root tricks** are the very important topics in any competitive exam. The **Square and Square roots** are the most commonly asked questions any government and private recruitment exam. Here we are providing the questions and answers according to the previous year question paper. The Square and Square Root Tricks are the most effective tricks for time management in any exam. We are learning the Square and Square root tricks from our school days.

Here we are explaining the Square and Square Root tricks by 50 digits of math. Kindly read carefully and remember all the short formulas like:

**1 ^{2} = 1 11^{2}=121 21^{2}=441 31^{2}=961**

**2 ^{2}=4 12^{2}=144 22^{2}=484 32^{2}=1024**

**3 ^{2}=9 13^{2}=169 23^{2}=529 33^{2}=1089**

**….. …… …….. ……..**

**Square and Square Root Problems and Solutions According to Previous year Papers:**

**Question 1: **Calculate the (55)^{2}=?

**Solution: **Consider a=5 and b=5

Applying Formula a^{2}+2ab+b^{2}

Or we can write

a^{2}/2ab/b^{2}= 5^{2}/2X5X5/5^{2}

=25/50/25

Note down 5 and Carry 2 by going from Right to Left

Now Add 2 with 50=52 Note down 2 at left of 5 and carry 5

Add Carry with 25 and (5+25)=30 Note down 30 at left of 2

(55)^{2}=3025

**Question 2:** Find Out the (57)^{2}??

**Solution:** Consider a=5 and b=7

Applying Formula a^{2}+2ab+b^{2}

Or we can write

a^{2}/2ab/b^{2}= 5^{2}/2X5X7/7^{2}

=25/50/49

Note down 9 and Carry 4 by going from Right to Left

Now Add 4 with 70=74 Note down 4 at left of 5 and carry 7

Add Carry with 25 and (7+25)=32 Note down 34 at left of 4

(55)^{2}=3249

**Question 3:** Find Out the (69)^{2}??

**Solution: **Consider a=6 and b=9

Applying Formula a^{2}+2ab+b^{2}

Or we can write

a^{2}/2ab/b^{2}= 6^{2}/2X6X9/9^{2}

=36/108/81

Note down 1 and Carry 8 by going from Right to Left

Now Add 1 with 108+8=116 Note down 6 at left of 1 and carry 11

Add Carry 11 with 36 and (11+36)=47 Note down 47 at left of 6

(69)^{2}=4761

**Question 4:** Find Out the (84)^{2}??

**Solution:** Consider a=8 and b=4

Applying Formula a^{2}+2ab+b^{2}

Or we can write

a^{2}/2ab/b^{2}= 8^{2}/2X8X4/4^{2}

=64/64/16

Note down 6 and Carry 1 by going from Right to Left

Now Add 1 with 64+1=65 Note down 5 at left of 5 and carry 6

Add Carry with 64 and (6+64)=70 Note down 70 at left of 5

(84)^{2}=7056

**Question 5:** Find Out the (76)^{2}??

**Solution:** Consider a=7 and b=6

Applying Formula a^{2}+2ab+b^{2}

Or we can write

a^{2}/2ab/b^{2}= 7^{2}/2X7X6/6^{2}

=49/84/36

Note down 6 and Carry 3 by going from Right to Left

Now Add 3 with 84=87 Note down 6 at left of 6 and carry 8

Add Carry with 49 and (8+49)=57 Note down 57 at left of 7

(76)^{2}=5776