Square & Square Roots


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1 Squre & Squre Roots Squre : If nuber is ultiplied by itself then the product is the squre of the nuber. Thus the squre of is x = eg. x x Squre root: The squre root of nuber is one of two equl fctors which is ultiplied together gives tht nuber. eg. = x = 0000 = 00 x 00 = 00 Finding Squre root by ens of fctoristion When given nuber is perfect squre, we resolve it into prie fctors nd tke the product of prie fctors, choosing one out of ech pir. eg. Find the squre root of Fctors of is xxx =xxx= x = x = x = Generl ethod to find the squre root In the given nuber rk off the digits in pirs, fro right nd then find the squre root s shown in the exple below. eg.. Find the squre root of,, 0 =. Find the squre root of =. Properties of perfect squre No perfect squre ends with,,, No perfect squre ends with n odd nuber of zeros. The perfect squre consisting of (n) or n digits will hve n root digits in their The squre of nuber other thn unity is either ultiple of or exceeds ultiple of by. CUBE ROOT The cube root of nuber is one of three equl fctors which if ultiplied gives tht nuber. Cube root of nuber cn be found out by using the following steps.. Write down ll the prie fctors of the given nubers.. Write the prie fctors in the index nottion, ie, in n for.. Divide the index by, then the result will be the cube root of the given nuber.
2 eg.. Find the cube root of =(xx) x (xx) x (xx) = ( ). Find the cube root of = Lern by hert the following squre roots SQUARES AND CUBES No. Squre Cube No Squre =. =. =.0 =. =. 0 0 =. PRACTICE TEST. If x= 0 + +, the vlue of xis. If x= ) d). x0., the vlue of xis. x0. ) d) 0.. If x, the vlue of x is ) d). If x = of x is. the vlue ) 0 d) ) x x 0.?. If x.., the vlue of xis ) d) d),00,000 0 x? ) 0. d).? + = % of 00. If x= ) d), the vlue of xis 0. 0 ) d) The lrgest of four digit nubers which is perfect squre is ) d) 0. A certin nuber of people collected Rs.. If ech person contributed s ny five pise s they re in nuber, the nuber of person were ) d)
3 . A grdener plnts n orchrd with trees. In ech row there were s ny trees s the nuber of rows. Find the nuber of rows. ) d). Ech student in clss contributed s ny rupees s the nuber of studnets in the clss for picnic. The school contributed Rs. 0 per techer who led the trip. If the totl ount collected ws Rs. 0 nd the nuber of techers who led the trip ws, how ny students were there in tht clss? ) d) 0. Soe persons contributed Rs. 0. Ech person gve s ny rupees s they re in nuber. Find their nuber. ) d) x. If then xis equl to. ) 0 d).. )? is equl to ) d) d). If 0. 0x0. x = 0.00 x 0. x b, then b is ) x0  x0  x0  d) x0 . The vlue of ()  0 d) is 0. The vlue of 0 0 is ) d). if. nd., the vlue of is )... d).. If then the vlue of.. is )... d).. If 0 = to then the vlue of is ) d).. The expression equls ) d) ANSWERS TO PRACTICE TEST. (. (). (. (. (. (. (). (. ( 0. (). (. (). (d). (). (d).(. (). (. ( 0. (.(. (. (. ()
4 Lws of Exponents A long product xx... fctors cn be expressed, in short by nottion, where `' is clled the bse nd `' the power (or index or exponent) Thus xx... 0 fctors = 0. Definition : If is nturl nuber, then stnds for the product of `' fctors ech equl to `'. Property : x n = +n (eg. x = + = ) Property : n= n (eg. =  = ) n Property : ( ) (eg. ( ) Mening of : Any nonzero nuber rised to zero power is equl to. n ie. = where 0 eg. =. Negtive Index : If 0 then (eg. ) Frctionl Index : n n eg., If `' nd `b' re nonzero integers, `' nd `n' re rtionl nubers, then i). x ii). n n n n iii). n n iv). v). vi). b. b SOLVED EXAMPLES :. x x? x x x x. x? x. x x. Evlute x ( ) = = =. If, find the vlue of
5 ANSWERS TO PRACTICE TEST. (. (). (d). (. (. (d). (. (d). (d) 0. (. (d). (. (. (. (d). (). (d). If nd n re whole nubers such tht n, find the vlue of ( ) n, n n n ( ) ( ) PRACTICE TEST. is divided by, the reinder is ) d). ( ) ( ) equls ). If n, the vlue of n is d) ) d). If.x0 k =0.00,the vlue of k is ) d) . The unit's digit in the product of x x is ) d) x. If x, the vlue of x is ) d) n n. The vlue of x n ). If b b x x ) is, xis equl to d) d). A boy ws sked to write the vlue of x. He wrote it s. The difference between the obtined nd the ctul vlue is ) x x x d) Zero 0. 0 x ( ). is equl to ) d). If b b c 0 nd, b, nd c re positive integers, the vlue of c is ) 0 d) dt indequte 0.. ( ) x ( 0. ) is equl to ) x x d). If 0,then the vlue of xis ) d) 0. The siplifiction of ) d)  gives. The units digit in will be ) d) x equls ) d). The vlue of x is euql to: ) d)
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