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The simplified value of 400тАЛ+0.09тАЛтИТ1.44тАЛ is
18.9
19.1
19.3
19.5
19.1
Calculate the roots individually (20,0.3,1.2) and perform addition/subtraction. Notice the unit digit: 20.0+0.3тИТ1.2 ends in 0+3тИТ2=1, helping you quickly identify 19.1.
An expression containing square roots of a whole number and two decimal numbers: 400тАЛ+0.09тАЛтИТ1.44тАЛ.
x2тАЛ=x,aтЛЕbтАЛ=aтАЛтЛЕbтАЛ
Calculate the roots individually (20,0.3,1.2) and perform addition/subtraction. Notice the unit digit: 20.0+0.3тИТ1.2 ends in 0+3тИТ2=1, helping you quickly identify 19.1.
Misplacing the decimal point when calculating 0.09тАЛ (some students mistake it for 0.9 instead of 0.3) or 1.44тАЛ (1.2 vs 0.12).
Evaluate individual square roots
Calculate the value of each term: 400тАЛ=20, 0.09тАЛ=1009тАЛтАЛ=0.3, and 1.44тАЛ=100144тАЛтАЛ=1.2.
400тАЛ=20,0.09тАЛ=0.3,1.44тАЛ=1.2
Substitute and simplify the expression
Substitute the evaluated roots into the original expression: 20+0.3тИТ1.2.
20+0.3тИТ1.2
Final calculation
Add 20 and 0.3 to get 20.3, then subtract 1.2 to obtain 19.1.
20.3тИТ1.2=19.1
B is correct because the step-by-step simplification of the square roots results in 20+0.3тИТ1.2=19.1.
Mastering the square roots of perfect squares up to 30 and their decimal counterparts is essential for speed in Data Interpretation and Simplification sections of competitive exams.