# RS Aggarwal Class 8 Math Third Chapter Squares and Square Roots Exercise 3C Solution

## EXERCISE 3C

**Find the value of the following, using the column method:**

**(1) (23) ^{2}**

Solution: Given number 23 = 20 + 3

Here, a = 20 and b = 3

a^{2} |
2ab | b^{2} |

(20)^{2} = 400 |
2 × 20 × 3 = 120 | (3)^{2} = 9 |

∴ (23)^{2} = (400 + 120 + 9) = 529

**(2) (35) ^{2}**

Solution: Given number 35 = 30 + 5

Here, a = 30 and b = 5

a^{2} |
2ab | b^{2} |

(30)^{2} = 900 |
2 × 30 × 5 = 300 | (5)^{2} = 25 |

∴ (35)^{2} = (900 + 300 + 25) = 1225.

**(3) (52) ^{2}**

Solution: Given number 52 = 50 + 2

Here, a = 50 and b = 2

a^{2} |
2ab | b^{2} |

(50)^{2} = 2500 |
2 × 50 × 2 = 200 | (2)^{2} = 4 |

∴ (52)^{2} = (2500 + 200 + 4) = 2704.

(4) (96)^{2}

Solution: Given number 96 = 90 + 6

Here, a = 90 and b = 6

a^{2} |
2ab | b^{2} |

(90)^{2} = 8100 |
2 × 90 × 6 = 1080 | (6)^{2} = 36 |

∴ (23)^{2} = (8100 + 1080 + 36) = 9216.

**Find the value of each of the following, using the diagonal method:**

**(5) (67) ^{2}**

**(6) (86) ^{2}**

**(7) (137) ^{2}**

**(8) (256) ^{2}**