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Square Root Calculator

Square Root Calculator

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What is a square root?

The square root of a number is the number that would have to be multiplied by itself to get the original number.
For example, the square root of 9 is 3 as 3 multiplied by 3 is 9.
The square root of 558,009 is 747, as 747 multiplied by 747 is 558,009.< The square root of 8 is 2.8284271247461900976033774484194 as 2.8284271247461900976033774484194 multiplied by 2.8284271247461900976033774484194 is 8.

How to calculate square root

Even for perfect square numbers, square root can be difficult to calculate by hand.
The most basic techniques involve trial and error.
Example:
Find the square root of 64
1) Try a number – 5 : 5 times 5 = 25 (too low)
2) Try another number that is more than 5 – 6 : 6 times 6 = 36 (too low)
3) Try a number that is more than 6 – 10 – 10 times 10 = 100 (too high)
4) Try a number in between 6 and 10 – 8 – 8 times 8 = 64 (answer)

What is square root used for?

From a practical standpoint, in geometry square root can be used to find the length of a side of a square when the area is known.

Table

Square root of 0 (√0) = 0.00000000000000000000
Square root of 1 (√1) = 1.00000000000000000000
Square root of 2 (√2) = 1.41421356237309514547
Square root of 3 (√3) = 1.73205080756887719318
Square root of 4 (√4) = 2.00000000000000000000
Square root of 5 (√5) = 2.23606797749978980505
Square root of 6 (√6) = 2.44948974278317788134
Square root of 7 (√7) = 2.64575131106459071617
Square root of 8 (√8) = 2.82842712474619029095
Square root of 9 (√9) = 3.00000000000000000000
Square root of 10 (√10) = 3.16227766016837952279
Square root of 11 (√11) = 3.31662479035539980998
Square root of 12 (√12) = 3.46410161513775438635
Square root of 13 (√13) = 3.60555127546398912486
Square root of 14 (√14) = 3.74165738677394132949
Square root of 15 (√15) = 3.87298334620741702139
Square root of 16 (√16) = 4.00000000000000000000
Square root of 17 (√17) = 4.12310562561766058565
Square root of 18 (√18) = 4.24264068711928477029
Square root of 19 (√19) = 4.35889894354067397586
Square root of 20 (√20) = 4.47213595499957961010
Square root of 21 (√21) = 4.58257569495583982899
Square root of 22 (√22) = 4.69041575982342973106
Square root of 23 (√23) = 4.79583152331271911351
Square root of 24 (√24) = 4.89897948556635576267
Square root of 25 (√25) = 5.00000000000000000000
Square root of 26 (√26) = 5.09901951359278449161
Square root of 27 (√27) = 5.19615242270663202362
Square root of 28 (√28) = 5.29150262212918143234
Square root of 29 (√29) = 5.38516480713450373941
Square root of 30 (√30) = 5.47722557505166118830
Square root of 31 (√31) = 5.56776436283002151839
Square root of 32 (√32) = 5.65685424949238058190
Square root of 33 (√33) = 5.74456264653802861631
Square root of 34 (√34) = 5.83095189484530074253
Square root of 35 (√35) = 5.91607978309961612950
Square root of 36 (√36) = 6.00000000000000000000
Square root of 37 (√37) = 6.08276253029821933893
Square root of 38 (√38) = 6.16441400296897601407
Square root of 39 (√39) = 6.24499799839839830895
Square root of 40 (√40) = 6.32455532033675904557
Square root of 41 (√41) = 6.40312423743284853117
Square root of 42 (√42) = 6.48074069840786037844
Square root of 43 (√43) = 6.55743852430200035997
Square root of 44 (√44) = 6.63324958071079961996
Square root of 45 (√45) = 6.70820393249936941515
Square root of 46 (√46) = 6.78232998312526813578
Square root of 47 (√47) = 6.85565460040104390771
Square root of 48 (√48) = 6.92820323027550877271
Square root of 49 (√49) = 7.00000000000000000000
Square root of 50 (√50) = 7.07106781186547550533
Square root of 51 (√51) = 7.14142842854285042620
Square root of 52 (√52) = 7.21110255092797824972
Square root of 53 (√53) = 7.28010988928051805402
Square root of 54 (√54) = 7.34846922834953453219
Square root of 55 (√55) = 7.41619848709566298339
Square root of 56 (√56) = 7.48331477354788265899
Square root of 57 (√57) = 7.54983443527074982171
Square root of 58 (√58) = 7.61577310586390865410
Square root of 59 (√59) = 7.68114574786860782041
Square root of 60 (√60) = 7.74596669241483404278
Square root of 61 (√61) = 7.81024967590665397665
Square root of 62 (√62) = 7.87400787401181112557
Square root of 63 (√63) = 7.93725393319377214851
Square root of 64 (√64) = 8.00000000000000000000
Square root of 65 (√65) = 8.06225774829854913150
Square root of 66 (√66) = 8.12403840463596083055
Square root of 67 (√67) = 8.18535277187245036146
Square root of 68 (√68) = 8.24621125123532117129
Square root of 69 (√69) = 8.30662386291807486316
Square root of 70 (√70) = 8.36660026534075562665
Square root of 71 (√71) = 8.42614977317635904797
Square root of 72 (√72) = 8.48528137423856954058
Square root of 73 (√73) = 8.54400374531753037388
Square root of 74 (√74) = 8.60232526704262667749
Square root of 75 (√75) = 8.66025403784438729815
Square root of 76 (√76) = 8.71779788708134795172
Square root of 77 (√77) = 8.77496438739212258895
Square root of 78 (√78) = 8.83176086632784773656
Square root of 79 (√79) = 8.88819441731558868014
Square root of 80 (√80) = 8.94427190999915922021
Square root of 81 (√81) = 9.00000000000000000000
Square root of 82 (√82) = 9.05538513813741730019
Square root of 83 (√83) = 9.11043357914429918765
Square root of 84 (√84) = 9.16515138991167965798
Square root of 85 (√85) = 9.21954445729288707412
Square root of 86 (√86) = 9.27361849549570393947
Square root of 87 (√87) = 9.32737905308881565247
Square root of 88 (√88) = 9.38083151964685946211
Square root of 89 (√89) = 9.43398113205660315828
Square root of 90 (√90) = 9.48683298050513812427
Square root of 91 (√91) = 9.53939201416945614653
Square root of 92 (√92) = 9.59166304662543822701
Square root of 93 (√93) = 9.64365076099295492895
Square root of 94 (√94) = 9.69535971483265868187
Square root of 95 (√95) = 9.74679434480896311754
Square root of 96 (√96) = 9.79795897113271152534
Square root of 97 (√97) = 9.84885780179610392793
Square root of 98 (√98) = 9.89949493661166535219
Square root of 99 (√99) = 9.94987437106619942995
Square root of 100 (√100) = 10.00000000000000000000

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