Use diagonal method to find the square of (i) 23 and (ii) 106
Answers
Answer:
1. Resolving 3675 into prime factors:
3675=3×5×5×7×7
Thus, to get a perfect square, the given number should be multiplied by 3.
New number= (32×52×72)=(3×5×7)2=(105)2
Hence, the new number is the square of 105.
2. Resolving 2156 into prime factors:
2156=2×2×7×7×11=(22×72×11)
Thus to get a perfect square, the given number should be multiplied by 11.
New number =(22×72×112)=(2×7×11)2=(154)2
Hence, the new number is the square of 154.
3. Resolving 3332 into prime factors:
3332=2×2×7×7×17=22×72×17
Thus, to get a perfect square, the given number should be multiplied by 17.
New number =(22×72×172)=(2×7×17)2=(238)2
Hence, the new number is the square of 238.
4. Resolving 2925 into prime factors:
2925=3×3×5×5×13=32×52×13
Thus, to get a perfect square, the given number should be multiplied by 13.
New number =(32×52×132)=(3×5×13)2=(195)2
Hence, the number whose square is the new number is 195.
5. Resolving 9075 into prime factors:
9075=3×5×5×11×11=3×52×112
Thus, to get a perfect square, the given number should be multiplied by 3.
New number =(32×52×112)=(3×5×11)2=(165)2
Hence, the new number is the square of 165.
6. Resolving 7623 into prime factors:
7623=3×3×7×11×11=32×7×112
Thus, to get a perfect square, the given number should be multiplied by 7.
New number =(32×72×112)=(3×7×11)2=(231)2
Hence, the number whose square is the new number is 231.
7. Resolving 3380 into prime factors:
3380=2×2×5×13×13=22×5×132
Thus, to get a perfect square, the given number should be multiplied by 5.
New number =(22×52×132)=(2×5×13)2=(130)2
Hence, the new number is the square of 130.
8. Resolving 2475 into prime factors:
2475=3×3×5×5×11=32×52×11
Thus, to get a perfect square, the given number should be multiplied by 11.
New number =(32×52×112)=(3×5×11)2=(165)2
Hence, the new number is the square of 165.
Step-by-step explanation:
1. Resolving 3675 into prime factors:
3675=3×5×5×7×7
Thus, to get a perfect square, the given number should be multiplied by 3.
New number= (32×52×72)=(3×5×7)2=(105)2
Hence, the new number is the square of 105.
2. Resolving 2156 into prime factors:
2156=2×2×7×7×11=(22×72×11)
Thus to get a perfect square, the given number should be multiplied by 11.
New number =(22×72×112)=(2×7×11)2=(154)2
Hence, the new number is the square of 154.
3. Resolving 3332 into prime factors:
3332=2×2×7×7×17=22×72×17
Thus, to get a perfect square, the given number should be multiplied by 17.
New number =(22×72×172)=(2×7×17)2=(238)2
Hence, the new number is the square of 238.
4. Resolving 2925 into prime factors:
2925=3×3×5×5×13=32×52×13
Thus, to get a perfect square, the given number should be multiplied by 13.
New number =(32×52×132)=(3×5×13)2=(195)2
Hence, the number whose square is the new number is 195.
5. Resolving 9075 into prime factors:
9075=3×5×5×11×11=3×52×112
Thus, to get a perfect square, the given number should be multiplied by 3.
New number =(32×52×112)=(3×5×11)2=(165)2
Hence, the new number is the square of 165.
6. Resolving 7623 into prime factors:
7623=3×3×7×11×11=32×7×112
Thus, to get a perfect square, the given number should be multiplied by 7.
New number =(32×72×112)=(3×7×11)2=(231)2
Hence, the number whose square is the new number is 231.
7. Resolving 3380 into prime factors:
3380=2×2×5×13×13=22×5×132
Thus, to get a perfect square, the given number should be multiplied by 5.
New number =(22×52×132)=(2×5×13)2=(130)2
Hence, the new number is the square of 130.
8. Resolving 2475 into prime factors:
2475=3×3×5×5×11=32×52×11
Thus, to get a perfect square, the given number should be multiplied by 11.
New number =(32×52×112)=(3×5×11)2=(165)2
Hence, the new number is the square of 165.