Surds and Indices

ABC26GN1882 · If x=ya, y=zb and z=xc, then find the value of abc.

ABC26GN1883 · Simplify : (xa/xb)^ (a2+b2+a b) × (xb/xc)^ (b2+c2+b c) × (xc/xa)^ (c2+a2+c a).

ABC26GN1903 · Which of the following expressions has the greatest value?

ABC26GN1905 · The value of (256)5/4 is

ABC26GN1887 · If x=3+2 √(2), find the value of (√(x)-1/(√(x))).

ABC26GN1906 · The value of (√(8))1/3 is

ABC26GN1907 · The value of (32/243)-4/5 is

ABC26GN1908 · The value of (-1/216)-2/3 is

ABC26GN1912 · The value of (0.03125)-2/5 is · 2006

ABC26GN1913 · (1/2)-1/2 is equal to · 2005

ABC26GN1956 · If x=5+2 √(6), then √(x)-1/(√(x)) is · 2009

ABC26GN1957 · (4+√(7)), expressed as a perfect square, is equal to (Section Officers', 2005)

ABC26GN1958 · √(8-2 √(15)) is equal to · 2007

ABC26GN1959 · √(6-4 √(3)+√(16-8 √(3))) is equal to · 2010

ABC26GN1960 · The value of 1/(√(12-√(140)))-1/(√(8-√(60)))-2/(√(10+√(84))) is · 2005

ABC26GN1961 · The value of the expression √(4+√(15))+√(4-√(15))-√(12-4 √(5)) is

ABC26GN1962 · If N=(√(√(5)+2)+√(√(5)-2))/(√(√(5)+1))-√(3-2 √(2)), then the value of N is · 2009

ABC26GN1974 · The expression ((x+1/y)a · (x-1/y)b)/((y+1/x)a · (y-1/x)b) reduces to

ABC26GN1976 · If x1/p=y1/q=z1/r and x y z=1, then the value of p+q+r would be · 2008

ABC26GN1977 · If ax=by=cz and b2=a c, then y equals

ABC26GN1978 · If ax=b, by=c and cz=a, then the value of x y z is · 2008

ABC26GN1980 · Suppose 4a=5, 5b=6, 6c=7, 7d=8, then the value of abcd is (A.A.O. Exam, 2009)

ABC26GN1988 · If 3x=5y=45z, then · 2002

ABC26GN1995 · If x=5+2 √(6), then ((x-1))/(√(x)) is equal to

ABC26GN1996 · If x1/3+y1/3=z1/3, then {(x+y-z)3+27 x y z} equals