# Quants Questions: Hacks on Square of a Number

Quantitative Aptitude is hard in most cases especially in exams like Banks and Insurance. Many Banks exam has a two-tier examination pattern i.e., Prelims and Mains. Most of them have changed their exam patterns and set a sectional timing of 20 minutes on each section. Quantitative aptitude is important for every exam because proper strategy and enough practice can help you score full marks in this section. There may not be assured in the language section and you may be stuck while solving reasoning questions but quants is a scoring subject and assure full marks if the calculation is correct.

So to help you ace the quants and to save your precious time during exam hours Adda247 providing some quant tricks to help aspirants.

Square of a numbers-

**1. Square from 20-30**

(21)

^{2 }= 4**41**, (22)^{2}= 4**84**, (23)^{2}=5**29**, (24)^{2}=5**76**, (25)^{2}=6**25**

Now tens and unit digit of a number repeats after (25)

(26)

^{2}=6**76**, (27)^{2}=7**29**, (28)^{2}=7**84**, (29)^{2}=8**41**.*Note- last 2 digits repeat here after the square of 25.*

**2. Square from 30-40**

(30)

^{2}=30*30=**900**
Use this formula to calculate the square:

**(a+b)**^{2}= a^{2}+b^{2}+2ab
(31)

^{2}= (30+1)^{2}= (30)^{2}+1+2*30*1)= 900+ 1+ 60=**961**
(32)

^{2}= (30+2)^{2}= (30)^{2}+ (2)^{2}+2*30*2=900+4+120=**1024**.**or we can write 32 as (2)**

^{5}=(32)^{2}=[(2)^{5}]^{2}=(2)^{10}= 1024 this is an important number.
.

**3**.

**Square from 40-50:**

The square from 40-50,

**unit and tens places**of square decreases from the square of 10 to 1.(40)

^{2}= 1600, (41)

^{2}= 1681, (42)

^{2}= 1764, (43)

^{2}= 1849, (44)

^{2}= 1936, (46)

^{2}= 2116

(45)

^{2}= 2025

**or we can calculate it by-**

**a) (45)**

^{2}= tens digit*(tens digit+1)**b) 25 as constant**

**c) sum of (difference of digits*50)= 2025**

(46)

^{2}= 2116, (47)^{2}= 2209, (48)^{2}= 2304, (49)^{2}= 2401.**3. Square of a number between 50-60.**

(50)

Half of 50 i.e 25, add the unit digit to 25, square of the unit digit.

^{2}= 2500Half of 50 i.e 25, add the unit digit to 25, square of the unit digit.

(51)

^{2}= (half of 50)+1 and square of 1 i.e 26**01**
(52)

^{2}=( half of 50)+2 and square of 2 i.e 27**04**
(53)

^{2}= (Half of 50)+3 and square of 3 i.e 28**09**
(54)

^{2}= 29**16.**
(55)

^{2}= 30**25**.**Or**you can find the square of 55 by**a) (55)**

^{2}= tens digit*(tens digit+1)**b) 25 as constant**

**c) sum of (difference of digits*50)= 3025.**

**6. Square of number multiple of 11.**

**step1. Count number of 1s.**

step2. then write the subsequent numbers of 1 till the number of 1s.

step3. then decrease the subsequent number.

(11)

^{2}=

**12**1 [ number of 1 is 2, write subsequent number till number of 1]

(111)2=

**123**21[ here number of one is 3],

(1111)

^{2}= 1234321[ here number of one is 4]

before further calculating square, you must know the shortcut to

**multiplication by 11.**

a)

**74*11**

step1. unit digit and the tens digit is as usual- (7_4)

step2. addition of digits- (7+4)

74*11= 814

b)

**46*11= 506**

**Now calculating more squares**

(22)

^{2}= 4*121 or 4*11*11=

**484**, (33)

^{2}= 9*121=

**1089**,

**(44)**

^{2}= 16*121= 16*11*11= 16*11=176*11multiplication of 176*11

step1. now 176*11= ones and tens digit (1 and 6) is as usual

step2. addition of (7&6)= 13 and take 3 and 1 is the carry

step3. addition of (1&7)= 8 and carry of step2 is added=9

so the multiplication of 176*11=

**1936**.

**Do it yourself-**

1. (222)

^{2}+(333)

^{2}

2. (66)

^{2}

3. (25)

^{2}+ (35)

^{2}+(45)

^{2}

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