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Question

Mathematics Question on Square Roots of Decimals

In a right triangle ABC, B∠ B = 90°.

  1. If AB = 6 cm, BC = 8 cm, find AC
  2. If AC = 13 cm, BC = 5 cm, find AB
Answer

(a) ABC\triangle ABC is right-angled at BB.
Therefore, by applying Pythagoras theorem, we obtain
AC2=AB2+BC2AC^2 = AB^2 + BC^2
AC2=(6cm)2+(8cm)2AC^2 = (6 cm)^2 + (8 cm)^2
AC2=(36+64)cm2AC^2 = (36 + 64) cm^2
=100100 cm2cm^2
AC=(100)cm=(10×10)cmAC = (\sqrt{100}) cm = (\sqrt{10 × 10}) cm
AC=10  cmAC = 10 \;cm


(b) ABC\triangle ABC is right-angled at BB.
Therefore, by applying Pythagoras theorem, we obtain
AC2=AB2+BC2AC^2 = AB^2+ BC^2
(13cm)2=(AB)2+(5cm)2(13 cm)^2= (AB)^2+ (5 cm)^2
AB2=(13cm)2(5cm)2AB^2= (13 cm)^2- (5 cm)^2
=(16925)cm2 (169 - 25) cm^2
= 144  cm2144 \;cm^2
AB=(144)cm=(12×12)cmAB = (\sqrt{144}) cm = (\sqrt{12 × 12}) \,cm
AB=12  cmAB = 12 \;cm