JAMB 1990 · UME · Q26

Surds

Given that $x^2 + y^2 + z^2 = 194$ , calculate $z$ if $x = 7$ and $\sqrt y = 3$ .

Worked solution (try it first)

Square both sides of $\sqrt y = 3$ : $y = 9$ , so $y^2 = 81$ .
Also $x^2 = 49$ .
Substitute: $49 + 81 + z^2 = 194$ , so $z^2 = 194 - 130 = 64$ .
Take the square root: $z = 8$ , option B.

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