Find the square root of following numbers without actual multiplication.
i] 39
ii] 42
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Find the square root of following numbers without actual multiplication.
i] 39
ii] 42
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Answer:
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This is your answer.
Step-by-step explanation:
39^2 = 39 × 39
= ( 30 + 9 ) × ( 30 + 9 )
= 30 ( 30 + 9 ) + 9 ( 30 + 9 )
= 30 × 30 + ( 30 × 9 ) + ( 9 × 30 ) + 9 × 9
= 900 + 270 + 270 + 81
= 1521
42^2 = 42 × 42
= ( 40 + 2 ) × ( 40 + 2 )
= 40 × ( 40 + 2 ) + 2 × ( 40 + 2 )
= 1600 + 80 + 80 + 4
= 1764
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Verified answer
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Square of 39 :
[tex]\bf{→{39}^{2}~=~1521}[/tex]
[tex]\rm{→{[30~+~9]}^{2}~=~30[30~+~9]~+~9[30~+~9]}[/tex]
[tex]\rm{→{30}^{2}~+~30~×~9~+~9~×~30~+~{9}^{2}}[/tex]
[tex]\rm{→900~+~270~+~270~+~81~=~1521}[/tex]
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Square of 42 :
[tex]\bf{→{42}^{2}~=~1764}[/tex]
[tex]\rm{→{[40~+~2]}^{2}~=~40[40~+~2]~+~2[40~+~2]}[/tex]
[tex]\rm{→{40}^{2}~+~40~×~2~+~2~×~40~+~{2}^{2}}[/tex]
[tex]\rm{→1600~+~80~+~80~+~4~=~1764}[/tex]
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