Mathematics
Square root spiral
Practice questions
In the square root spiral, the point ( \sqrt{16} ) lies at which integer distance?Why is the square root spiral considered useful for representing irrational numbers on the number line?If a unit perpendicular is added to the radius \( \sqrt{24} \), the new hypotenuse will be closest to which integer?A student wrote the next hypotenuse after \( \sqrt{6} \) as \( \sqrt{6}+1 \). What is the correct correction?Which triangle is formed while constructing ( \sqrt{3} ) from ( \sqrt{2} ) in the square root spiral?If ( \sqrt{30} ) has been constructed in the square root spiral, what will be the new hypotenuse in the immediate next construction?Which option gives the correct order of the first four hypotenuse lengths in the square root spiral?What is the simplified form of the distance ( \sqrt{50} ) in the square root spiral?If the old radius of a triangle is ( \sqrt{35} ), between which two integers will the new hypotenuse lie?In the triangle that constructs ( \sqrt{15} ) in the square root spiral, what are the old radius and the new side?If (OP_n=\sqrt{n}), what is the difference between the squares of (OP_{n+3}) and (OP_n)?At which step does the new hypotenuse become equal to \(2\sqrt{3}\)?What form is obtained after simplifying the radius \( \sqrt{40} \) in the square root spiral?If the spiral is constructed up to ( \sqrt{48} ), why will the final distance lie between (6) and (7)?In a square root spiral, (OP_4=2). What does this correctly mean?If the radius \( \sqrt{63} \) is formed, what simplified form is it equal to?What is the difference between the squares of radii \( \sqrt{5} \) and \( \sqrt{13} \) in the square root spiral?If \( \sqrt{72} \) is formed in the spiral, what is (a) when it is written as \(a\sqrt{2}\)?Why does the next step after ( \sqrt{n} ) become ( \sqrt{n+1} ) in a square root spiral?If the point \( \sqrt{80} \) is on the spiral, between which two consecutive integers is its distance?