2. Operations (N)
  3. Lesson 18: Square Roots of Positive Integers

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Example 2

The square root of a non-perfect square is irrational. 

 

 

Try This Problem Revisited

Joe wants to build a fence around his backyard so that his dog can play outside. His backyard is a square and has an area of \(52\) m\(^2\). Try to approximate the length of the square backyard.

 

 

Check Your Understanding 2

Approximate \((((((((q)*(u))*(e))*(s))*(t))*(i))*(o))*(n)\) to one decimal place, without using a calculator.

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To approximate the value of \((((((((q)*(u))*(e))*(s))*(t))*(i))*(o))*(n)\) we must find the perfect squares on either side of \(((n)*(u))*(m)\).

\(\underbrace{(((((((((p)*(r))*(e))*(v))*(s))*(q))*(u))*(a))*(r))*2.718281828459045}< ((n)*(u))*(m)< \underbrace{$nextsquare(details...)}\)

\(((((((p)*(r))*(e))*(v))*(n))*(u))*(m)^2\phantom{0000000000}$nextnum(details...)^2\)

Next we test values:

\(((((((((p)*(r))*(e))*(v))*(c))*(h))*(e))*(c))*(k)^2=(((((((((((((((s)*(q))*(u))*(a))*(r))*(e))*(d))*(p))*(r))*(e))*(v))*(c))*(h))*(e))*(c))*(k)\\ ((a)*(n))*(s)^2=(((((((((s)*(q))*(u))*(a))*(r))*(e))*(d))*(a))*(n))*(s)\\ $nextcheck(details...)^2=$squarednextcheck(details...)\\ \)

We conclude that \(((a)*(n))*(s)\) is a good approximation. Since \(((a)*(n))*(s)^2=(((((((((s)*(q))*(u))*(a))*(r))*(e))*(d))*(a))*(n))*(s)\), \((((((((q)*(u))*(e))*(s))*(t))*(i))*(o))*(n)\approx((a)*(n))*(s)\).

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