Question

Find the difference using a property of square numbers {(n+1) 2 – n 2 = (n+1) + n} i) 30 2 - 29 2 ii) 87 2 - 86 2

Answer 1

(i) $(30^{2} -29^{2} )$ = 59.

(ii) $(87^{2} -86^{2} )$ = 173.

Step-by-step explanation:

We are given with the following property of square numbers to use in solving the questions below;

The property is: $(n+1)^{2} - n^{2} = (n + 1) + n$

(i) The first part says we have to find the difference of $(30^{2} -29^{2} )$;

By seeing the property we can observe that in this question (n = 29), i.e;

    $(29+1)^{2} -29^{2}$  =  $(29+1) + 29$     {comparing with the property}

                             = 30 + 29 = 59.

Hence, the difference of $(30^{2} -29^{2} )$ = 59.

(ii) The second part says we have to find the difference of $(87^{2} -86^{2} )$;

By seeing the property we can observe that in this question (n = 86), i.e;

    $(86+1)^{2} -86^{2}$  =  $(86+1) + 86$     {comparing with the property}

                             = 87 + 86 = 173.

Hence, the difference of $(87^{2} -86^{2} )$ = 173.